bluuebunny/crossref_metadata_2025 huggingface dataset:
Onf(n) modulo Ω(n) and ω(n) whenfis a polynomial
Authors: Luca Florian
Published: April 2009

In this paper we show that iff(X) ∈; Z [X ] is a nonzero polynomial, then ω(n)/f(n)holds only on a set ofnof asymptotic density zero, where for a positive integernthe number ω(n) counts the number of distinct prime factors ofn.
Integral points on elliptic curves over function fields
Authors: Chi W. -C. , Lai K. F. , Tan K. -S.
Published: April 2009

We prove a new formula for the number of integral points on an elliptic curve over a function field without assuming that the coefficient field is algebraically closed. This is an improvement on the standard results of Hindry-Silverman.
Ergodicity and stability of orbits of unbounded semigroup representations
Authors: Basit Bolis , Pryde A. J.
Published: April 2009

We develop a theory of ergodicity for unbounded functions ø: J → X, where J is a subsemigroup of a locally compact abelian group G and X is a Banach space. It is assumed that ø is continuous and dominated by a weight w defined on G. In particular, we establish total ergodicity for the orbits of an (unbounded) strongly continuous representation T: G → L(X) whose dual representation has no unitary point spectrum. Under additional conditions stability of the orbits follows. To study spectra of functions, we use Beurling algebras L1w(G) and obtain new characterizations of their maximal primary ideals, when w is non-quasianalytic, and of their minimal primary ideals, when w has polynomial growth. It follows that, relative to certain translation invariant function classes , the reduced Beurling spectrum of ø is empty if and only if ø ∈ . For the zero class, this is Wiener's tauberian theorem.
The size of characters of exceptional lie groups
Authors: Hare Kathryn E. , Yeats Karen
Published: April 2009

Pointwise bounds for characters of representations of the compact, connected, simple, exceptional Life groups are obtained. It is a classical result that if μ is a central, continuous measure on such a group, then μdimG is absolutely continuous. Our estimates on the size of characters allow us to prove that the exponent, dimension of G, can be replaced by approximately the rank of G. Similar results were obtained earlier for the classical, compact Lie groups.
The wake of a finite rotating disc
Authors: Leslie L. M.
Published: April 2009

When a disc rotates in a fluid at rest, fluid near the disc acquires azimuthal momentum because of the viscous torque of the disc and outwards radial momentum under the action of centrifugal forces. The resultant flow is essentially a swirling jet. Away from the disc continuity requires the existence of an axial flow towards the disc to compensate for the fluid which has been thrown outwards. If the disc is finite there is a discontinuity in the boundary conditions at the edge of the disc where the no-slip condition is suddenly replaced by a condition of zero stress in the plane of the disc. The flow discharged from the edge of the disc is essentially a wake embedded in a swirling radial jet. It appears that no investigation of this wake has yet been made.
Factorization of hyponormal operators
Authors: Embry Mary R.
Published: April 2009

In [1]R. G. Douglas proved that if A and B are continuous linear operators on a Hilbert space X, the following three conditions are equivalent:
Projective bitopological spaces
Authors: Datta M. C.
Published: April 2009

J. C. Kelly [2] introduced the concept of a bitopological space. Lane [3], Patty [4] and Pervin [5] have continued his work. Our purpose in this paper is to identify the projective objects in a suitable category of bitopological spaces after the manner of Gleason [1] and generalize his theorem that in the category of compact Hausdoriff topological spaces, the projective spaces are precisely the extremally disconnected ones.
Dispersal in compact semimodules
Authors: Wallace Alexander Doniphan
Published: April 2009

A semigroup is a nonvoid Hausdorff space together with a continuous associative operation. A semiring is a nonvoid Hausdorff space together with a couple of continuous associative operations, one of which (usually denoted as multiplication) distributes over the other (usually denoted as addition). If R is a semiring then an R-semimodule is a semigroup M under addition together with a continuous operation R × M → M which satisfies the associativity and distributivity conditions usually stipulated in the instance of an R-module. It is purpose of this paper to establish for semimodules certain propositions proved by Kaplansky [4], Pearson [8], Selden [9], Beidleman-Cox [1] and others.
Skew connections in vector bundles and their prolongations
Authors: Virsik Juraj
Published: April 2009

The paper is closely related to [1] and [2]. A skew connection in a vector bundleEas defined here is a pseudo-connection (in the sense of [1]) which can be changed into a connection by transforming separately the bundleEitself and the bundle of its differentials, i.e. one-forms on the base with values inE. The properties of skew connections are thus expected to be only “algebraically” more complicated than those of connections; especially one can follow the pattern of [1], and prolong them to obtain higher order semi-holonomic and non-holonomic pseudo-connections. It is shown in this paper that under some circumstances the main theorem of [1] or [2] applies also to skew connections.
On intersections and unions of radical classes
Authors: Lee Yu-Lee , Propes R. E.
Published: April 2009

Let A be a class of rings, and let L(A) denote the lower radical class determined by A. In [3] Yu-Lee Lee showed that L(A) may b constructed in the following manner: Let H(A) be the class of all homomorphic images of rings in A.
On the construction of the Kurosh lower radical class for associative rings
Authors: Kreiling Daryl , Jenkins Terry L.
Published: April 2009

All rings considered are to be associative. For definitions not included in this paper see [2]. Let R be a ring and S a subring of R.
The subnormal structure of some classes of coluble groups
Authors: McDougall D.
Published: April 2009

Finite groups in which normality is transitive have been studied by Best and Taussky, [1], Gaschütz, [3], and Zacher [16]. Infinite soluble groups in which normality is transitive have been studied by Robinson in [9]. A subgroupHof a groupGis subnormal inGifHcan be connected toGby a chain ofrsubgroups, in which each is normal in its successor, whereris a non-negative integer. The least suchris called the subnormal index ofHinG(or the defect ofHinG). Then groups in which normality is transitive are precisely those in which every subnormal subgroup has subnormal index at most one. Thus the structure of soluble groups in which every subnormal subgroup has subnormal index at mostn(such a group is said to have bounded subnormal indices) has been dealt with by Robinson in [9] for the case wherenis one. However Theorem D of [12] states that a soluble group of derived lengthncan be embedded in a soluble group in which the subnormal indices are at mostn. Therefore we must impose further conditions on the groups if we hope to obtain any worthwhile results for the above problem withngreater than one.
The SQ-universality of some finitely presented groups
Authors: Neumann Peter M.
Published: April 2009

Following a suggestion of G. Higman we say that the group G is SQ-universal if every countable group is embeddable in some factor group of G. It is a well-known theorem of G. Higman, B. H. Neumann and Hanna Neumann that the free group of rank 2 is sq-universal in this sense. Several different proofs are now available (see, for example, [1] or [9]). It is my intention to prove the LEmma. If H is a subgroup of finite index in a group G, then G is SQ-universal if and only if H is SQ-universal.
A construction of rings whose injective hulls allow a ring structure
Authors: Dlab Vlastimil , Ringel Claus Michael
Published: April 2009

In her paper [3], Osofsky exhibited an example of a ring R containing 16 elements which (i) is equal to its left complete ring of quotients, (ii) is not self-injective and (iii) whose injective hull HR = H(RR) allows a ring structure extending the R-module structure of HR. In the present note, we offer a general method of constructing such rings; in particular, given a non-trivial split Frobenius algebra A and a natural n ≧ 2, a certain ring of n x n matrices over A provides such an example. Here, taking for A the semi-direct extension of Z/2Z by itself and n = 2, one gets the example of Osofsky. Thus, our approach answers her question on finding a non-computational method for proving the existence of such rings.
The third term of the lower central series of a free group as a subgroup of the second
Authors: Ward Martin
Published: April 2009

In this paper the following notation will be used: for any group G, positive integer c and non-negative integer n, Gc is the cth term of the lower central series of G and δ nGc is the nth term of the derived series of Gc.
The simple groups related to M24, II
Authors: Held Dieter
Published: April 2009

The objective of this paper is to prove the following generalization of the main result in [2]: THeorem. Let G be a finite simple group which possesses an involution t such that the centralizer of t in G is isomorphic to the centralizer of an involution in H. Then G is isomorphic to L5(2), M24, or H.
Some infinitely based varieties of groups
Authors: Bryant Roger M.
Published: April 2009

Problem 11 of Hanna Neumann's book [3] asks whether the product variety Β4Β2 has a finite basis for its laws. (For any positive integer k, Βk denotes the variety of all groups of exponent diving k.) I think that Β4Β2 was being suggested as a plausible canditate for a variety without the finite basis property; of course, at a time when no such example was known. It is the primary object of this note to verify the fact that Β4Β2 is not finitely based. Β4Β2 provides, therefore, probably the simplest example known at present of a variety which is not finitely based.
Lattice automorphisms of semi-simple Lie algebras
Authors: Barnes D. W.
Published: April 2009

Let L be a Lie algebra over the field F. A lattice automorphism of ℒ is an automorphism φ: ℒ(L) → ℒ(L) of the lattice ℒ(L) of all subalgebras of L. We seek to describe the lattice automorphisms in terms of maps σ: L→L of the underlying algebra. A semi-automorphism σ of L is an automorphism of the algebraic system consisting of the pair (F, L), that is, a pair of maps σ: F→ F, σ: L→ L preserving the operations. Thus σ: F → F is an automorphism of F and (x + y)σ = xσ + yσ, (xy)σ = xσyσ (λx)σ = λσxσ for all x, y ε L and λ ε F. Clearly, any semi-automorphism of L induces a lattice automorphism. To study a given lattice automorphism φ, we select a semi-automorphism a such that φσ-1 fixes certain subalgebras, and so we reduce the problem to the investigation of lattice automorphisms leaving these subalgebras fixed.
Permutable subgroups of some finite p-groups
Authors: Stonehewer S. E.
Published: April 2009

A subgroup H of a group G is said to be a permutablesubgroup of G if HK = KH 〈H, K〉 for all subgroups K of G. It is known that a core-free permutable subgroup H of a finite group G is always nilpotent [5]; and even when G is not finite, H is always a subdirect product of finite nilpotent groups [11]. Thus nilpotency is a measure of the extent to which a permutable subgroup differs from being normal. Examples of non-abelian, core-free, permutable subgroups are rare and difficult to construct. The first, due to Thompson [12], had class 2. Further examples of class 2 appeared in [8]. More recently Bradway, Gross and Scott [1] have constructed corresponding to each positive integer c and each prime p ≥ c, a finite p-group possessing a core-free permutable subgroup of class c. In [3] Gross succeeded in dispensing with the requirement p ≥ c.
The double cover relative to a convex domain and the relative isoperimetric inequality
Authors: Choe Jaigyoung
Published: April 2009

We prove that a domain Ω in the exterior of a convex domain C in a four-dimensional simply connected Riemannian manifold of nonpositive sectional curvature satisfies the relative isoperimetric inequality 64π2 Vol(Ω)3 < Vol(∂Ω ~ ∂C)4. Equality holds if and only if Ω is an Euclidean half ball and ∂Ω ~ ∂C is a hemisphere.
The inverse limit of some free algebras
Authors: Allen A. L. , Moran S.
Published: April 2009

Let Ω[x1, x2, …, xn] denote the algebra of polynomials in variables x1, x2, …, xn with coefficients from a fixed field Ω of characteristic zero, where n = 1, 2,…. There exists a natural projection which maps xn onto 0 and all the other variables onto themselves, for n = 1, 2, …. This enables one to construct the corresponding inverse limit which we here denote by Ω[x]. The algebra Ω[x] has a natural degree function defined on it.
On one-factorizations of complete graphs
Authors: Wallis W. D.
Published: April 2009

We use standard graph notation and definitions, as in [1]: in particular Kn is the complete graph on n vertices and Kn, n is the regular complete bigraph of order 2n.
On duality in complex linear programming
Authors: Craven B. D. , Mond B.
Published: April 2009

In [3], Levinson proved a duality theorem for linear programming in complex space. Ben-Israel [1] generalized this result to polyhedral convex cones in complex space. In this paper, we give a simple proof of Ben-Israel's result based directly on the duality theorem for linear programming in real space. The explicit relations shown between complex and real linear programs should be useful in actually computing a solution for the complex case. We also give a simple proof of Farkas' theorem, generalized to polyhedral cones in complex space ([1], Theorem 3.5); the proof depends only on the classical form of Farkas' theorem for real space.
A p-adic analogue to a theorem by J. Popken
Authors: Mahler K.
Published: April 2009

It is proved that if is a formal power series with algebraic p-adic coefficients which satisfies an algebraic differential equation, then a constant y4 > 0 and a constant integer h1 ≧ 0 exist such that .
Basic p-groups: higher commutator structure
Authors: Weichsel Paul M.
Published: April 2009

The classification of groups according to the varieties they generate requires the study of a class of indecomposable elements. Such a class is the class of basic groups which have been studied in [4], [5] and [6]. A group is called basic if it is indecomposable qua group; that is, it is critical and indecomposable qua variety; that is, its variety is join-irreducible. In this note we consider the higher commutator structure of basic p-groups. Our main theme is the relation between the formal weight of the higher commutator subgroups and the class of the group. We obtain information about the power-commutator structure of a basic p-group, the kinds of laws that can hold in such a group and the varietal structure of groups of the form: Center-extended-by-X.
A lattice analogue of a theorem of Chow
Authors: Maxwell George
Published: April 2009

LetKbe a skewfield,Ea left vector space overK,ran integer ≧ 1 andGr(E)the set of all r-dimensional subspaces of E, called the Grassmannian of index r. The functiond(A, B) =r— dim (A∩B) is a distance onGr(E). If K′ is a skewfield and E′ a left vector space overK1, then any semilinear ismorphismu:E→E1(relative to an isomorphism K → K') induces a distance preserving bijectionGr(u):Gr(E) → Gr(E′). WhenEhas finite dimensionnand 2r=n, another example of such a mapping is obtained by takingK′ = Kop, E′ = E* and definingwr: Gr(E) → Gr(E*)to bewr(A)= {f∈E*&f(A)= 0}.
The existence of Fano subplanes in generalized Hall planes
Authors: Rahilly A. J.
Published: April 2009

One of the best known classes of non-Desarguesian planes is the calss of Hall planes (see Hall [2]). In [6] Hanna Neumann showed that the finite Hall planes of old order possess subplanes of order two (i.e., Fano subplanes)1. Kirkpatrick [5] has considered a type of plane which is generalization of the Hall planes and which he calls generalized Hall planes. In this paper we will give a sufficient condition that a finite generalized Hall plane possesses Fano subplanes. Some examples of odd order planes to which the condition applies shall be exhibited.
On finitely injective modules
Authors: Ramamurthi V. S. , Rangaswamy K. M.
Published: April 2009

A right module A over a ring R is called finitely injective if every diagram of right R-modules of the form where X is finitely generated and the row is exact, can be imbedded in a commutative diagram The finitely injective modules turn out to have the nice property of being ‘strongly pure’ in all the containing modules and, in particular, are absolutely pure in the sense of Maddox [8]. For this reason we call them strongly absolutely pure (for short, SAP) modules. Several other characterizations of the SAP modules are obtained. It is shown that every module admits a ‘SAP hull’. The concepts of finitely M-injective and finitely quasi-injective modules are then investigated. A subclass of finitely quasi-injective modules, called the strongly regular modules, is studied in some detail and it is shown that, if R/J is right Noetherian, then the strongly regular right R-modules coincide with the semi-simple R-modules.
The Gelfand transform of homogeneous distributions on Heisenberg type groups
Authors: Astengo Francesca , Blasio Bianca Di
Published: April 2009

A distribution on a Heisenberg type group of homogeneous dimension Q is a biradial kernel of type α if it coincides with a biradial function, homogeneous of degree α — Q, and smooth away from the identity. We prove that a distribution is a biradial kernel of type α, 0 < α < Q, if and only if its Gelfand transform, defined on the Heisenberg fan, extends to a smooth even function on the upper half plane, homogeneous of degree −α/2. A similar result holds for radial kernels on the Heisenberg group.
Filter games and pathological subgroups of a countable product of lines
Authors: Banakh Taras , Nickolas Peter , Sanchis Manuel
Published: April 2009

To each filter ℱ on ω, a certain linear subalgebra A(ℱ) of Rω, the countable product of lines, is assigned. This algebra is shown to have many interesting topological properties, depending on the properties of the filter ℱ. For example, if ℱ is a free ultrafilter, then A(ℱ) is a Baire subalgebra of ℱω for which the game OF introduced by Tkachenko is undetermined (this resolves a problem of Hernández, Robbie and Tkachenko); and if ℱ1 and ℱ2 are two free filters on ω that are not near coherent (such filters exist under Martin's Axiom), then A (ℱ1) and A(ℱ2) are two o-bounded and OF-undetermined subalgebras of ℱω whose product A(ℱ1) × A(ℱ2) is OF-determined and not o-bounded (this resolves a problem of Tkachenko). It is also shown that the statement that the product of two o-bounded subrings of ℱω is o-bounded is equivalent to the set-theoretic principle NCF (Near Coherence of Filters); this suggests that Tkachenko's question on the productivity of the class of o-bounded topological groups may be undecidable in ZFC.
Normal characterization by zero correlations
Authors: Seneta Eugene , Szekely Gabor J.
Published: April 2009

Suppose Xi, i = 1,…,n are indepedent and identically distributed with E/X1/r < ∞, r = 1,2,…. If Cov (( − μ)r, S2) = 0 for r = 1, 2,…, where μ = EX1, S2 = , and , then we show X1 ~ N (μ, σ2), where σ2 = Var(X1). This covariance zero condition charaterizes the normal distribution. It is a moment analogue, by an elementary approach, of the classical characterization of the normal distribution by independence of and S2 using semi invariants. More generally, if Cov = 0 for r = 1,…, k, then E((X1 − μ)/σ)r+2 = EZr+2 for r = 1,… k, where Z ~ N(0, 1). Conversely Corr may be arbitrarily close to unity in absolute value, but for unimodal X1, Corr2( < 15/16, and this bound is the best possible.
C*-algebras associated with presentations of subshifts ii. ideal structure and lambda-graph subsystems
Authors: Matsumoto Kengo
Published: April 2009

A λ-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. InDoc. Math.7 (2002) 1–30, the author constructed aC*-algebraO£associated with a λ-graph system £ from a graph theoretic view-point. If a λ-graph system comes from a finite labeled graph, the algebra becomes a Cuntz-Krieger algebra. In this paper, we prove that there is a bijective correspondence between the lattice of all saturated hereditary subsets of £ and the lattice of all ideals of the algebraO£, under a certain condition on £ called (II). As a result, the class of theC*-algebras associated with λ-graph systems under condition (II) is closed under quotients by its ideals.
The Weighted g-drazin inverse for operators
Authors: Dajić A. , Koliha J. J.
Published: April 2009

The paper introduces and studies the weighted g-Drazin inverse for bounded linear operators between Banach spaces, extending the concept of the weighted Drazin inverse of Rakočević and Wei (Linear Algebra Appl. 350 (2002), 25–39) and of Cline and Greville (Linear Algebra Appl. 29(1980), 53–62). We use the Mbekhta decomposition to study the structure of an operator possessing the weighted g-Drazin inverse, give an operator matrix representation for the inverse, and study its continuity. An open problem of Rakočević and Wei is solved.
Two-sided ideals in group near-rings
Authors: Meyer J. H.
Published: April 2009

The two-sided ideals of group near-rings are characterized and studied. Various examples are presented to illustrate the interplay between ideals in the base near-ring R and the corresponding group near-ring R[G]. Some results concerning the Jacobson radicals of R[G] are also discussed.
Homomorphisms of nonzero degree betweenPDn-groups
Authors: Hillman Jonathan A.
Published: April 2009

We give algebraic proofs of some results of Wang on homomorphisms of nonzero degree between aspherical closed orientable 3-manifolds. Our arguments apply toPDn-groups which are virtually poly-Zor have a Kropholler decomposition into parts of generalized Seifert type, for alln.
On quasinilpotent Operators, II
Authors: Foiaş Ciprian , Jung Il Bong , Ko Eungil , Pearcy Carl
Published: April 2009

In this paper we continue to modify and expand a technique due to Enflo for producing nontrivial hyperinvariant subspaces for quasinilpotent operators, and thereby obtain such subspaces for some additional quasinilpotent operators on Hilbert space. We also obtain a structure theorem for a certain class of operators.
A dual differentiation space without an equivalent locally uniformly rotund norm
Authors: Kenderov Petar S. , Moors Warren B.
Published: April 2009

A Banach space (X, ∥ · ∥) is said to be a dual differentiation space if every continuous convex function defined on a non-empty open convex subset A of X* that possesses weak* continuous subgradients at the points of a residual subset of A is Fréchet differentiable on a dense subset of A. In this paper we show that if we assume the continuum hypothesis then there exists a dual differentiation space that does not admit an equivalent locally uniformly rotund norm.
An LP version of Hardy's theorem for the Dunkl transform
Authors: Gallardo Léonard , Trimèche Khalifa
Published: April 2009

In this paper, we give a generalization of Hardy's theorems for the Dunkl transform ℱD on ℝd. More precisely for all a > 0, b > 0 and p, q ∈ [1, + ∞], we determine the measurable functions f on ℝd such that where are the Lebesgue spaces associated with the Dunkl transform.
Modular Lie representations of finite groups
Authors: Bryant R. M.
Published: April 2009

Let K be a field of prime characteristic p and let G be a finite group with a Sylow p-subgroup of order p. For any finite-dimensional K G-module V and any positive integer n, let Ln (V) denote the nth homogeneous component of the free Lie K-algebra generated by (a basis of) V. Then Ln(V) can be considered as a K G-module, called the nth Lie power of V. The main result of the paper is a formula which describes the module structure of Ln(V) up to isomorphism.
The commutator subgroup and Schur multiplier of a pair of finite p-groups
Authors: Salemkar Ali Reza , Moghaddam Mohammad Reza R. , Saeedi Farshid
Published: April 2009

Let (M, G) be a pair of groups, in which M is a normal subgroup of G such that G/M and M/Z(M, G) are of orders pm and pn. respectively. In 1998, Ellis proved that the commutator subgroup [M, G] has order at most pn(n + 2 m−1)/2.

In the present paper by assuming /[M, G] = pn(n+2m−1)/2, we determine the pair (M, G). An upper bound is obtained for the Schur multiplier of the pair (M, G), which generalizes the work of Green (1956).
Finite Fourier series and ovals in PG(2, 2h)
Authors: Fisher J. Chris , Schmidt Bernhard
Published: April 2009

We propose the use of finite Fourier series as an alternative means of representing ovals in projective planes of even order. As an example to illustrate the method's potential, we show that the set {wj + w3j + w−3j: 0 ≤ j ≤ 2h} ⊂ GF (22h) forms an oval if w is a primitive (2h + 1)st root of unity in GF(22h) and GF(22h) is viewed as an affine plane over GF(2h). For the verification, we only need some elementary ‘trigonometric identities’ and a basic irreducibility lemma that is of independent interest. Finally, we show that our example is the Payne oval when h is odd, and the Adelaide oval when h is even.
Strict convexity of sets in analytic terms
Authors: Dalla Leoni , Hatziafratis Telemachos
Published: April 2009

We compare the geometric concept of strict convexity of open subsets of Rn with the analytic concept of 2-strict convexity, which is based on the defining functions of the set, and we do this by introducing the class of 2N-strictly convex sets. We also describe an exhaustion process of convex sets by a sequence of 2-strictly convex sets.
Estimates for kernels of intertwining operators on SL(n, R)
Authors: Cowling Michael , Meda Stefano
Published: April 2009

In this paper we study the kernels and the Lp–Lq boundedness properties of some intertwining operators associated to representations of SL(n, R).
Multialgebras, universal algebras and identities
Authors: Pelea Cosmin , Purdea Ioan
Published: April 2009

In this paper we determine the smallest equivalence relation on a multialgebra for which the factor multialgebra is a universal algebra satisfying a given identity. We also establish an important property for the factor multialgebra (of a multialgebra) modulo this relation.
On symmetric ideals of multilinear mappings between Banach spaces
Authors: Botelho Geraldo , Pellegrino Daniel M.
Published: April 2009

In this paper we provide examples and counterexamples of symmetric ideals of multilinear mappings between Banach spaces and prove that if I1, …, In are operator ideals, then the ideals of multilinear mappings L(I1, …, In) and /I1, …, In/ are symmetric if and only if I1 = … = In.
Continuous bijections on manifolds
Authors: Doyle P. H. , Hocking J. G.
Published: April 2009

The main results of the paper give necessary and sufficient conditions as well as sufficient conditions that continuous bijections of a manifold onto itself be homeomorphisms. Such conditions include the embedding of manifolds, preserving ends, preserving closed half-rays and restrictions on boundary components. A number of counterexamples are given to likely conjectures.
Finitely generated subgroups of amalgamated free products and HNN groups
Authors: Cohen Daniel E.
Published: April 2009

The theory of groups acting on trees due to Bass and Serre (1969) is applied to simplify some results of Burns (1972, 1973) giving conditions under which an amalgamated free product or HNN extension has the properties that any finitely generated subgroup containing an infinite subnormal subgroup must have finite index and that the intersection of two finitely generated subgroups is finitely generated.
On the infinite divisibility of the von Mises distribution
Authors: Lewis Toby
Published: April 2009

It is shown, by use of a Bochner-type condition for infinite divisibility, that the von Mises distribution is infinitely divisible for some values of the concentration parameter k, certainly for k < 0.16.
Compatible tight Riesz orders on C(X)
Authors: Loci Elizabeth
Published: April 2009

The pointwise order makes the group C(X) of continuous real-valued functions on a topological space X a lattice-ordered group. We give a characterization of the compatible tight Riesz orders on C(X), and also of their maximal tangents, in terms of the zero-sets of X. The space of maximal tangents of a given compatible tight Riesz order T is studied, and consequently the concept of the T-radical of C(X) is introduced, the T-radical being the intersection of all the maximal tangents of T.
Characterizations of a generalized notion of compactness
Authors: Butcher George H. , Joseph James E.
Published: April 2009

This paper gives theorems which encompass known characterizations of many of the generalized compactness properties.
Conjugate purity and infinite groups
Authors: Balogun Bola O.
Published: April 2009

In Balogun (1974), we proved that a finite group in which every subgroup is conjugately pure is necessarily Abelian and we left open the infinite case. In this paper we settle this problem positively for soluble, locally soluble groups and certain classes of groups which include the FC-groups. In the last section of this paper we characterize groups which are conjugately pure in every containing group.

Subject classification (Amer. Math. Soc. (MOS) 1970): 20 E 99.
The automorphism group of the semigroup of finite complexes of a periodic abelian group
Authors: Byrd R. D. , Lloyd J. T. , Stepp J. W.
Published: April 2009

In this paper it is shown that ifGis a periodic Abelian group and ∣G∣ ≥ 6, then the only automorphisms of the semigroup of finite nonempty complexes ofGare induced by automorphisms ofG.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 20 M 15; secondary 20 K 30.
On Sylow graphs
Authors: Holton D. A. , Sheehan J.
Published: April 2009

We characterize the classes of graphs of order n whose automorphism group either contains or coincides with the 2-Sylow subgroup of the symmetric group Sn.

Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 25.
Order-bounded convergence structures on spaces of continuous functions
Authors: Schroder M.
Published: April 2009

This paper deals with solid topologies and convergence structures on the vector-lattice CX (the set of all continuous real-valued functions on a space X): the closed ideals and locally convex topologies associated with such structures are studied in particular. The work stems from E. Hewitt's paper on bounded linear functionals, touches on the classical theorems of L. Nachbin, T. Shirota and others (determining when the topology of compact convergence is barrelled or bornological), and extends some recent results on the duality between x and CX.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 54 C 35; secondary 54 A 20.
When is the iterate of a formal power series odd?
Authors: Reznick Bruce
Published: April 2009

The formal power series (fps) f(z) = Σ∞i=1ai zi is homozygous mod k if ai ≠ 0 implies i ≡ j mod k. This generalizes even and odd fps. If f is homozygous mod k then all iterates of f (fn = f ο fn−1) are also homozygous mod k, but the converse is false–there are many non-odd fps f for which f(f(z)) = z. It is shown that if f is not homozygous mod k but fn is homozygous, then fnr(z) = z for some r. If all coefficienrs ar real then, in fact, f(f(z)) = z.

Subject classification (Amer. Math Soc. (MOS) 1970): 39 A 05.
Solutionally complete varieties
Authors: Hule Harald
Published: April 2009

A veristy is called solutionally complete if any solvable system of algebraic equations over an algebra A in which has at most one solution in every extension of A in has the solution in A. A necessary and sufficient condition for solutional completeness is given which is a weaker form of the strong amalgamation property.

Subject classification (Amer. Math. Soc. (MOS) 1970): 08 A 15.
On characters in the principal 2-block, II
Authors: Herzog Marcel , Praeger Cheryl E.
Published: April 2009

Let k be a non-zero complex number and let u and v be elements of a finite group G. Suppose that at most one of u and v belongs to O(G), the maximal normal subgroup of G of odd order. It is shown that G satisfies X(v)–X(u) = k for every complex nonprincipal irreducible character X in the principal 2-block of G, if and only if G/O(G) is isomorphic to one of the following groups: C2, PSL(2, 2n) or pΣL(2, 52a+1), where n≥2 and a ≥ 1.

Subject classification (Amer. Math. Soc. (MOS) 1970): 20 C 20
Integral starlike trees
Authors: Watanabe Mamoru , Schwenk Allen J.
Published: April 2009

In this note we determine which of the trees homeomorphic to a star have a spectrum consisting entirely of integers. We also specify the integral double stars, and we consider the problem of trees with more complicated structure.

Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 05.
A note on BIBD's
Authors: Wallis Jennifer
Published: April 2009

A balanced incomplete block design or BIBD is defined as an arrangement of v objects in b blocks containing k objects all different, so that there are r blocks containing a given object and λ blocks containing any two given objects.
Lipschitz conditions and lacunarity
Authors: Edwards R. E.
Published: April 2009

We consider 2π-periodic functions on the limits and give simple and complete characterizations, in terms of Fourier coefficients, of functions which belong to various Lipschitz classes and whose Fourier series are lacunary. Such characterisations seem to be missing from the literature, though there are various wellknown partial characterisations valid for functions with arbitrary spectra; cf. the remarks following Theorem 1. The results given below form complements to and sharpenings of some of the standard results valid for the special case of lacunary series.
Asymptotically quasi-compact products of bounded linear operators
Authors: Ruston Anthony F.
Published: April 2009

It is known (see, for instance, [1] p. 64, [6] p. 264) that, if A and B are bounded linear operators on a Banach space into itself (or, more generally, if A is a bounded linear operator on into a Banach space and B is a bounded linear operator on into), then AB and BA have the same spectrum except (possibly) for zero. In the present note, it is shown that AB is asymptotically quasi-compact if and only if BA is asymptotically quasi-compact, and that then any Fredholm determinant for AB is a Fredholm determinant for BA and vice versa.
The free product of skew fields
Authors: Cohn P. M.
Published: April 2009

In a recent paper [3] it was shown that the free product K * L of two fields (possibly skew) can be embedded in a field, and moreover, this latter can be chosen to be the ‘universal field of fractions’ of K*L (cf. [4, 5]). This opens up the prospect of doing for skew fields what the Neumanns and others have done for groups; indeed some sample applications were given in [3]. We pursue this topic here a little further: our main results state (i) every ccuntably generated field can be embedded in a 2-generator field, (ii) in a free product of rings over a field k, any element algebraic over k is conjugate to an element in one of the factors, (iii) any field can be embedded in a field with nth roots for each n. These results are all analogous to well known results in group theory (cf. [8]), and although the proofs are not just a translation of the group case, the latter is of scme help. Thus (ii), (iii) follow fairly easily, but they lead to other problems, still open, by replacing ‘free product of rings’ in (ii) by ‘field product of fields, and in (iii) replacing ‘nth roots’ by ‘roots of any equation’. On the other hand, (i) is less immediate, since ‘field products’ need to be used in the proof, and their manipulation requires some more technical lemmas.
Bigenetic properties of finitely generated hyper- (Abelian-by-finite) groups
Authors: Lennox J. C.
Published: April 2009

Let be a class and p a property of groups. We say that p is a bigenetic property of p-groups (or more simply, p is bigenetic in p-groups) if an p-group G has the property p whenever all two-generator subgroups of G have p.
The subnormal coalescence of some classes of groups of finite rank
Authors: Drukker Mark , Robinson Derek J. S. , Stewart Ian
Published: April 2009

A class of groups forms a (subnormal) coalition class, or is (subnormally) coalescent, if wheneverHandKare subnormal -subgroups of a groupGthen their join  is also a subnormal -subgroup ofG. Among the known coalition classes are those of finite groups and polycylic groups (Wielandt [15]); groups with maximal condition for subgroups (Baer [1]); finitely generated nilpotent groups (Baer [2]); groups with maximal or minimal condition on subnormal subgroups (Robinson [8], Roseblade [11, 12]); minimax groups (Roseblade, unpublished); and any subjunctive class of finitely generated groups (Roseblade and Stonehewer [13]).
Some small aspherical spaces
Authors: Dyer Eldon , Vasquez A. T.
Published: April 2009

LetSndenote the sphere of all points in Euclidean space Rn+ 1at a distance of 1 from the origin andDn+ 1the ball of all points inRn+ 1at a distance not exceeding 1 from the origin The spaceXis said to beasphericalif for everyn≧ 2 and every continuous mapping:f:Sn→X, there exists a continuous mappingg:Dn+ 1→Xwith restriction to the subspaceSnequal tof. Thus, the only homotopy group ofXwhich might be non-zero is the fundamental group τ1(X, *) ≅G. IfXis also a cell-complex, it is called aK(G, 1). IfXandYareK(G, l)'s, then they have the same homotopy type, and consequently
Compactifications of semitopological semigroups II
Authors: Milnes Paul
Published: April 2009

Correcting some “proofs” given in an earlier paper of the same title, we prove here, among other things, that, if S is a subgroup of a topological group that is complete in a left invariant metric or locally compact, then every weakly almost periodic function on S is (left and right) uniformly continuous. We also prove a theorem related to results of R. B. Burckel and of W. W. Comfort and K. A. Ross: a topological group is pseudocompact if and only if WAP(G) = C(G).
Regularly varying solutions of a linear functional equation
Authors: Kuczma Marek
Published: April 2009

We are concerned with the problem of the existence and uniqueness of regularly varying (in Karamata's sense) solutions ϕ of the linear functional equation in a right neighbourhood of x = 0. Under suitable conditions on the given functions f and h, the uniqueness of solutions depends essentially on whether the series Σh ∘ f1 converges or diverges; here fi denotes the i-th functional iterate of f. The existence of solutions may be proved under further assumptions.

The case of the more general linear functional equation may be reduced to that of equation (*).
Remark on a paper by Aczél and Ostrowski
Authors: Walter Wolfgang
Published: April 2009

The objective of the paper Aczél and Ostrowski (1973) is to show in an elementary way that any real-valued function f, defined on (0,1) and satisfying he inquality , where n ≧ 3 is fixed, is necessary of the form .
Some exact solutions of certain field equations in general relativity
Authors: Patel L. K.
Published: April 2009

A general metric is considered. Some solutions correspoding to the field equations Rik λgik = −8πEik are obtained as particular cases. Details of these solutions are also discussed. An Einstein space corresponding to the field equations Rik = λ gik is also constructed as a particular case of the general metric.
An entire function which has wandering domains
Authors: Baker I. N.
Published: April 2009

Let f(z) denote a rational or entire function of the complex variable z and fn(z), n = 1,2, …, the n−th iterate of f. Provided f is not rational of order 0 or 1, the set of those points where {fn(z)} forms a normal family is a proper subset of the plane and is invariant under the map z → f(z). A component G of is a wandering domain of f if fn(G)∩fn(G) = Ø for all k ≧ 1, n ≧ 1, k ≠ n. The paper contains the construction of a transcendental entire function which has wandering domains.
A construction for certain classes of supplementary difference sets
Authors: Cooper Joan
Published: April 2009

Let ν = ef + 1 be a prime power, and consider G the cyclic group of order ν − 1 with e cosets Ci, of order f defined as Ci = {xej+i: 0 ≦ j ≦ f − 1} and 0 ≦ i ≦ e − 1, where x is a primitive element of GF(pα) and a generator of G. By using these cosets we give a simple construction for certain classes of Supplementary Difference Sets, Difference Sets, and Szekeres Difference Sets. These classes are not new, but the simple method of construction is original.
p-Groups with an Abelian Maximal Subgroup and Cyclic Center
Authors: Conlon S. B.
Published: April 2009

All such nonabelian finite p-groups are classified. They coincide with the class of nonabelian finite p-subgroups of GL(p, F), where F is a field, not of characteristic p, which contains all p power roots of 1, or agian with the class of all nonabelian finite subgroups of Zp= wr Zp. Various automorphism groups associated to them and their representations are calculated. Two such subgroups of GL(p, F) are conjugate as subgroups of GL(p, F) iff they are isomorphic.
Kernels of orthodox semigroup homomorphisms
Authors: Feigenbaum Ruth
Published: April 2009

Any congruence on an orthodox semigroup S induces a partition of the set E of idempotents of S satisfying certain normality conditions. Meakin (1970) has characterized those partitions of E which are induced by congruences on S as well as the largest congruence ρ and the smallest congruence σ on S corresponding to such a partition of E. In this paper a more precise description of ρ and σ is given.
The hulls of representablel-groups andf-rings
Authors: Conrad Paul
Published: April 2009

A lattice-ordered group (“l-group”)Gwill be called

aP-groupifG=g″ ⊕g′ for eachg∈G(projectable)

anSP-groupifG=C⊕C′ for each polarCofG(strongly projectable)

anL-groupif each disjoint subset has a 1. u. b. (laterally complete)

anO groupif it is both anL-groupand aP-group (orthocomplete).

Gisrepresentableif it is anl-subgroup of a cardinal product of totally ordered groups. It follows that aP-group must be representable and henceSP-groups andO-groups are also representable.
Quotient groups and realization of tight Riesz groups
Authors: Miller John Boris
Published: April 2009

Let (G, ≼) be an l-group having a compatible tight Riesz order ≦ with open-interval topology U, and H a normal subgroup. The first part of the paper concerns the question: Under what conditions on H is the structure of (G, ≼, ∧, ∨, ≦, U) carried over satisfactorily to by the canonical homomorphism; and its answer (Theorem 8°): H should be an l-ideal of (G, ≼) closed and not open in (G, U). Such a normal subgroup is here called a tangent. An essential step is to show that ≼′ is the associated order of ≦′.
Free inverse semigroups
Authors: Preston G. B.
Published: April 2009

In an important recent paper H. E. Scheiblich gave a construction of free inverse semigroups that throws considerable light on their structure [1]. In this note we give an alternative description of free inverse semigroups. What Scheiblich did was to construct a free inverse semigroup as a semigroup of isomorphisms between principal ideals of a semilattice E, say, thus realising free inverse semigroups as inversee subsemigroupss of the semigroup TE, a kind of inverse semigroup introduced and exploited by W. D. Munn [2]. We go instead directly to canonical forms for the elements of a free inverse semigroup. The connexion between our construction and that of Scheiblich's will be clear. There are several alternative procedures possible to reach our construction on which we comment on the way.
Two notes on Rankin's book on the modular group
Authors: Lyndon Roger
Published: April 2009

We supply proofs that are simple, and possibly partly new, for two theorems that appear in Rankin's book [6].
Finite group with Hall coverings
Authors: Jabara Enrico , Lucido Maria Silvia
Published: April 2009

In this paper we describe the groups admitting a covering with Hall subgroups. We also determine the groups with a π1-Hall subgroup, where π1 is the connected component of the prime graph, containing the prime 2.
On the value distribution of f2f(k)
Authors: Huang Xiaojun , Gu Yongxing
Published: April 2009

In this paper, we prove that for a transcendental meromorphic function f(z) on the complex plane, the inequality T(r, f) < 6N (r, 1/(f2 f(k)−1)) + S(r, f) holds, where k is a positive integer. Moreover, we prove the following normality criterion: Let ℱ be a family of meromorphic functions on a domain D and let k be a positive integer. If for each ℱ ∈ ℱ, all zeros of ℱ are of multiplicity at least k, and f2 f(k) ≠ 1 for z ∈ D, then ℱ is normal in the domain D. At the same time we also show that the condition on multiple zeros of f in the normality criterion is necessary.
U-Operators
Authors: Bernal-González L. , Prado-Tendero J. A.
Published: April 2009

Inspired by a statement of W. Luh asserting the existence of entire functions having together with all their derivatives and antiderivatives some kind of additive universality or multiplicative universality on certain compact subsets of the complex plane or of, respectively, the punctured complex plane, we introduce in this paper the new concept of U-operators, which are defined on the space of entire functions. Concrete examples, including differential and antidifferential operators, composition, multiplication and shift operators, are studied. A result due to Luh, Martirosian and Müller about the existence of universal entire functions with gap power series is also strengthened.
Further results on meromorphic functions that share two values with their derivatives
Authors: Yang Chung-Chun , Li Ping
Published: April 2009

In this paper we continue our previous studies and derive all possible expressions for a meromorphic function and its differential polunomials when they share two finite distinct values a1, a2, CM (counting multiplicities) in majority.
Effective bounds of the solutions of certain Diophantine equations
Authors: Feldman N. I.
Published: April 2009

The paper establishes an effective bound for the solutions of the equation, under some conditions.

Subject classification (Amer. Math. Soc. (MOS) 1970): 10 B 15.
On the existence of sulutions of the equationLx∞Nxand a coincidence degree theory
Authors: Tarafdar E. , Teo Suat Khoh
Published: April 2009

The coincidence degree for the pair (L, N) developed by Mawhin (1972) provides a method for proving the existence of solutions of the equationLx = NxwhereL: domL⊂X→Zis a linear Fredholm mapping of index zero andis a (possiblv nonlinear) mapping and Ω is a bounded open subset ofX, XandZbeing normed linear spaces over the reals. In this paper we have extended the coincidence degree for the pair (L, N) to solve the equation, whereL: domL⊂X→Zis a linear Fredholm mapping of index zero,andX, Zand Ω are as above,CK(Z)being the set of compact convex subsets ofZ.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 47 H 15, 47 A 50; secondary 47 H 10, 47 A 55.
Free groups, symmetric and reduced products
Authors: Borges Carlos R.
Published: April 2009

We show that, for any Tychonoff space X with base point θ, the infinite symmetric product SP∞ X of X is a subspace of an abelian group A(X) generated by X. (This clarifies the continuity of the multiplication in SP∞ X.) Furthermore, SP∞ X is a retract of A(X). Analogous results hold for reduced product spaces, with respect to non-abelian groups.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 22 A 99; secondary 54 B 15.
Universal functions in several complex variables
Authors: Chee P. S.
Published: April 2009

It is proved that there exists a universal good inner function in the open unit polydisc Un, that is its non Euclidean translates are dense in the closed unit ball of H∞ (Un) and that there exists a universal function in the open unit ball Bn of Cn. These generalize Heins' result on universal Blaschke products.

1980 Mathematics subject classification (Amer. Math. Soc.): primary 32 A 10.