bluuebunny/crossref_metadata_2025_split huggingface dataset:
Autoclinisms and automorphisms of finite groups II
Authors: Tappe Jürgen 
Published: May 2009

In part I of this paper P. Hall's formula for finite stem groups was derived. Using results of C. R. Leedham-Green and S. McKay, a similar formula for isoclinic groups with arbitrary branch factor group is shown.The main result of this paper is the following theorem, which appears without proof in [1, p. 203].
On the kernels of representations of finite groups
Authors: Koshitani Shigeo 
Published: May 2009

Let G be a finite group and p a prime number. About five years ago I. M. Isaacs and S. D. Smith [5] gave several character-theoretic characterizations of finite p-solvable groups with p-length 1. Indeed, they proved that if P is a Sylow p-subgroup of G then the next four conditions (l)–(4) are equivalent:(1) G is p-solvable of p-length 1.(2) Every irreducible complex representation in the principal p-block of G restricts irreducibly to NG(P).(3) Every irreducible complex representation of degree prime to p in the principal p-block of G restricts irreducibly to NG(P).(4) Every irreducible modular representation in the principal p-block of G restricts irreducibly to NG(P).
Some examples of modules over Noetherian rings
Authors: Musson I. M. 
Published: May 2009

The purpose of this note is to prove the following result.Theorem 1.Let n be an integer greater than zero. There exists a prime Noetherian ring R of Krull dimension n + 1 and a finitely generated essential extension W of a simple R-module V suchthat(i)W has Krull dimension n, and(ii)W/V is n-critical and cannot be embedded in any of its proper submodules.We refer the reader to [6] for the definition and properties of Krull dimension.
Lifting sets and the Calkin algebra
Authors: Murphy G. J. 
Published: May 2009

H will denote a Hilbert space of infinite dimension, ℬ(H) the algebra of bounded linear operators on H, and ℛ(H) the ideal of compact operators on H. We let σ, σe and σω denote the spectrum, essential spectrum and Weyl spectrum respectively. It is well known that for arbitrary T ∈ ℬ(H) we have by [5]andand
A class of maximal orders integral over their centres
Authors: Gray Andy J. 
Published: May 2009

In a recent paper [1], Brown, Hajarnavis and MacEacharn have considered non-commutative Noetherian local rings of finite global dimension which are integral over their centres. For such a ring Rthey have shown:(i) R is a prime ring whose Krull and global dimensions coincide;(ii) R = ∩ RP where p runs through the set of rank one primes of the centre of R, and each Rp is hereditary;(iii) the centre of R is a Krull domain.
On an integral equation of Šub-Sizonenko
Authors: Rooney P. G. 
Published: May 2009

The integral equation of the title isIt was studied in [4], though h(x) was written as x-1g(x-1) there, and using a method involving orthogonal Watson transformations, it was shown there that if h ∈ L2(0, ∞), then the equation has a solution f ∈ L2(0, ∞), and that / is given byIn this paper, using the techniques of [3], we shall show that the equation can be solved for ℎ in the space ℒμ, p of [3] for 1 ≤ p < ∘, μ > 0, and that for these spaces, which include L2(0, ∘), f is given by the simpler formulaWe shall further show that these results can be extended to the spaces ℒw, μ, p of [3]. This forms the content of our theorem below.
Addendum to a paper of M. Saks
Authors: Perfect Hazel 
Published: May 2009

Throughout, (X, ≤ ) denotes a partially ordered set (p. o. set), where X is assumed to be finite. A subset Y of X is called a k-union if Y contains no chain of length K + 1. In particular, therefore, a 1-union is just an antichain; and it is readily seen that Y is a k-union if and only if it is a union of K antichains. (Dually, a subset Z of X is a k-counion if Z contains no antichain of length k + 1.) We denote by dk (X) the maximum cardinality of a k-union in X, with a similar notation for other p. o. sets. Now let be any partition of X into chains, and write.
Embedding any countable semigroup in a 2-generated bisimple monoid
Authors: Byleen Karl 
Published: May 2009

G. B. Preston [10] proved that any semigroup can be embedded in a bisimple monoid. If S is a countable semigroup, his constructive proof yields a bisimple monoid which is also countable, but not necessarily finitely generated. The main result of this paper is that any countable semigroup can be embedded in a 2-generated bisimple monoid.J. M. Howie [6] proved that any semigroup can be embedded in an idempotentgenerated semigroup. F. Pastijn [9] showed that any semigroup can be embedded in a bisimple idempotent-generated semigroup, and that any countable semigroup can be embedded in a semigroup which is generated by 3 idempotents. Easy proofs of these results using Rees matrix semigroups over a semigroup were given by the author [3]. In this paper, as a corollary to our main result, we deduce that any countable semigroup can be embedded in a bisimple semigroup which is generated by 3 idempotents.
Generation of the lower central series II
Authors: Guralnick Robert M. 
Published: May 2009

In this article, we obtain results on commutators in Sylow subgroups of the lower central series, extending the work of Dark and Newell [2], Rodney [12, 13] and Aschbacher and the author [1, 6, 7].Some notation is required for the statement of the main results. Let r be a positive integer and defineandwhere x1, …, xr, are elements in a group G. Let ΓrG = {[x1, …, xr]∣ x1 ∈ G} be the set of r-fold commutators in G. Then Lr,G = 〈ΓrG〉 is the rth term in the lower central series of G. Set L∞G = ∩ Lr,G.
Free completely regular semigroups
Authors: Trotter P. G. 
Published: May 2009

A completely regular semigroup is a semigroup that is a union of groups. The aim here is to provide an alternative characterization of the free completely regular semigroup Fcrx on a set X to that given by J. A. Gerhard in [3, 4].Although the structure theory for completely regular semigroups was initiated in 1941 [1] by A. H. Clifford it was not until 1968 that it was shown by D. B. McAlister [5] that Fcrx exists. More recently, in [7], M. Petrich demonstrated the existence of Fcrx by showing that completely regular semigroups form a variety of unary semigroups (that is, semigroups with the additional operation of inversion).
Multiplier systems for Hilbert's and Siegel's modular groups
Authors: Gundlach Karl-Bernhard 
Published: May 2009

The classical generalizations (already investigated in the second half of last century) of the modular group SL(2, ℤ) are the groups ГK= SL(2,o)(othe principal order of a totally real number fieldK, [K:ℚ]=n), operating, originally, on a productofnupper half-planes or, forn=2, on the product1×−of an upper and a lower half-plane by(wherev(i), forv∈K, denotes the jth conjugate ofv), and Гn= Sp(n, ℤ), operating onn={Z∣Z=X+iY∈ℂ(n,n),tZ=Z, Y>0} byNowadays ГKis called Hilbert's modular group ofKand ГnSiegel's modular group of degree (or genus)n.Forn=1 we have Гℚ=Г1= SL(2, ℤ). The functions corresponding to modular forms and modular functions for SL(2, ℤ) and its subgroups are holomorphic (or meromorphic) functions with an invariance property of the formJ(L, t)for fixedL(orJ(M, Z)for fixedM) denoting a holomorphic function without zeros on) (or onn). A functionJ;, defined on ℤK×or ℤn×nto be able to appear in (1.3) withf≢0, has to satisfy certain functional equations (see below, (2.3)–(2.5) for ГK, (5.7)–(5.9) for Гn) and is called an automorphic factor (AF) then. In close analogy to the casen=1, mainly AFs of the following kind have been used:with a complex numberr, the weight ofJ, and complex numbersv(L), v(M). AFs of this kind are called classical automorphic factors (CAP) in the sequel. Ifr∉ℤ, the values of the functionvon ГK(or Гn) depend on the branch of (…)r. For a fixed choice of the branch (for eachL∈ГKorM∈Гn) the functional equations forJ, by (1.4), (1.5), correspond to functional equations forv.A functionvsatisfying those equations is called a multiplier system (MS) of weightrfor ГK(or Гn).
Small solutions of quadratic congruences
Authors: Heath-Brown D. R. 
Published: May 2009

Let Q(x) = Q(x1, …, xn)∈ℤ[x1, …, xn] be a quadratic form. We investigate the size of the smallest non-zero solution of the congruence Q(x)≡0 (mod q). We seek a bound Bn(q), independent of Q, such that there is always a non-zero solution satisfyingThe form gives the trivial lower bound Bn(q)≥(q/n)½ for all q and n, since if x≠0 and q∣ Q(x), then Q(x)≥q.
Joint spectra of operators on Banach space
Authors: Chō Muneo 
Published: May 2009

Let X be a complex Banach space. We denote by B(X) the algebra of all bounded linear operators on X. Let = (T1, …, Tn) be a commuting n-tuple of operators on X. And let στ() and σ″() by Taylor's joint spectrum and the doubly commutant spectrum of , respectively. We refer the reader to Taylor [8] for the definition of στ() and σ″(), A point z = (z1,…, zn) of ℂn is in the joint approximate point spectrum σπ() of if there exists a sequence {xk} of unit vectors in X such that∥(Ti – zi)xk∥→0 as k → ∞ for i = 1, 2,…, n.
Approximate point spectrum and commuting compact perturbations
Authors: Rakočević Vladimir 
Published: May 2009

Let X be an infinite-dimensional complex Banach space and denote the set of bounded (compact) linear operators on X by B (X) (K(X)). Let σ(A) and σa(A) denote, respectively, the spectrum and approximate point spectrum of an element A of B(X). Setσem(A)and σeb(A) are respectively Schechter's and Browder's essential spectrum of A ([16], [9]). σea (A) is a non-empty compact subset of the set of complex numbers ℂ and it is called the essential approximate point spectrum of A ([13], [14]). In this note we characterize σab(A) and show that if f is a function analytic in a neighborhood of σ(A), then σab(f(A)) = f(σab(A)). The relation between σa(A) and σeb(A), that is exhibited in this paper, resembles the relation between the σ(A) and the σeb(A), and it is reasonable to call σab(A) Browder's essential approximate point spectrum of A.
Non-abelian exterior products of groups and exact sequences in the homology of groups
Authors: Ellis G. J. 
Published: May 2009

Various authors have obtained an eight term exact sequence in homologyfrom a short exact sequence of groups,the term V varying from author to author (see [7] and [2]; see also [5] for the simpler case where N is central in G, and [6] for the case where N is central and N ⊂ [G, G]). The most satisfying version of the sequence is obtained by Brown and Loday [2] (full details of [2] are in [3]) as a corollary to their van Kampen type theorem for squares of spaces: they give the term V as the kernel of a map G ∧ N → N from a “non-abelian exterior product” of G and N to the group N (the definition of G ∧ N, first published in [2], is recalled below). The two short exact sequencesandwhere F is free, together with the fact that H2(F) = 0 and H3(F) = 0, imply isomorphisms..The isomorphism (2) is essentially the description of H2(G) proved algebraically in [11]. As noted in [2], the isomorphism (3) is the analogue for H3(G) of the Hopf formula for H2(G).
Generalisation de la decomposition de kato aux opérateurs paranormaux et spectraux
Authors: Mbekhta Mostafa 
Published: May 2009

Dans tout ce qui suit,Hdésigne un espace de Hilbert séparable,Aun opérateur fermé de domaineD(A) dansH, on noteB(H) l'ensemble des opérateurs bornés deHdans lui-même etN(A),R(A) respectivement le noyau deA, l'image deA.En 1958, T. Kato a démontré dans [7] le théorème suivant.
On weak approximation and convexification in weighted spaces of vector-valued continuous functions
Authors: Nawrocki Marek 
Published: May 2009

Let X be a completely regular Hausdorff space. A Nachbin family of weights is a set V of upper-semicontinuous positive functions on X such that if u, υ ∈ V then there exists w ∈ V and t > 0 so that u, υ ≤ tw. For any Hausdorff topological vector space E, the weighted space CV0(X, E) is the space of all E-valued continuous functions f on X such that υf vanishes at infinity for all υ ∈ V. CV0(X, E) is equipped with the weighted topologywv = wv(X, E) which has as a base of neighbourhoods of zero the family of all sets of the formwhere υ ∈ Vand W is a neighbourhood of zero in E. If E is the scalar field, then the space CV0(X, E) is denoted by CV0(X). The reader is referred to [4, 6, 8] for information on weighted spaces.
The equation y′ = fy in zero residue characteristic
Authors: Escassut Alain , Sarmant Marie-Claude 
Published: May 2009

Let K be an algebraically closed field complete with respect to an ultrametric absolute value |.| and let k be its residue class field. We assume k to have characteristic zero (hence K has characteristic zero too).Let D be a clopen bounded infraconnected set [3] in K, let R(D) be the algebra of the rational functions with no pole in D, let ‖.‖D be the norm of uniform convergence on D defined on R(D), and let H(D) be the algebra of the analytic elements on D i.e. the completion of R(D) for the norm ‖.‖D.
Toeplitz operators and algebras of bounded analytic functions on the disk
Authors: Smith R. C. 
Published: May 2009

Here and throughout, A is a closed subalgebra of H∞ that contains the disk algebra and M(A) denotes the maximal ideal space of A. Because A contains the function fo(z) = z, we can define the fiber Mλ(A) of M(A) for λ ε ∂D (the unit circle) in the usual way; i.e., Mλ(A) = {φ ∈ M(A): fo(φ) = λ}. The Bergman space of the unit disk D is the L2(D, dx dy)-closure of A. Let be the orthogonal projection. For f ∈ L∞(D, dx dy), define the multiplication operator Mf: L2(D, dx dy)→ L2, (D, dx dy) byand define the Toeplitz operator by
Interpolating sequences for the derivatives of Bloch functions
Authors: Attele K. R. M. 
Published: May 2009

AbstractWe prove that sufficiently separated sequences are interpolating sequences for f′(z)(1−|z|2) where f is a Bloch function. If the sequence {zn} is an η net then the boundedness f′(z)(1−|z|2) on {zn} is a sufficient condition for f to be a Bloch function. The essential norm of a Hankel operator with a conjugate analytic symbol acting on the Bergman space is shown to be equivalent to .
Unbounded approximate identities in normed algebras
Authors: Dixon P. G. 
Published: May 2009

The object of this paper is to consider two easy propositions concerning bounded approximate identities and show that they do not extend to unbounded approximate identities. The propositions are as follows.Proposition 1.1. Every bounded left approximate identity in a normed algebra is a left approximate identity for the completion.Proposition 1.2. Every bounded left approximate identity in a separable normed algebra has a subsequence which is a left approximate identity.
Normal closures of powers of Dehn twists in mapping class groups
Authors: Humphries Stephen P. 
Published: May 2009

LetF = F(g, n)be an oriented surface of genusg≥1withn<2boundary components and letM(F)be its mapping class group. ThenM(F)is generated by Dehn twists about a finite number of non-bounding simple closed curves inF([6, 5]). See [1] for the definition of a Dehn twist. Letebe a non-bounding simple closed curve inFand letEdenote the isotopy class of the Dehn twist aboute. LetNbe the normal closure ofE2inM(F). In this paper we answer a question of Birman [1, Qu 28 page 219]:Theorem 1.The subgroup N is of finite index in M(F).
Infinite dimensional representations of
Authors: Dean A. , Zorzitto F. 
Published: May 2009

By a representation of the extended Dynkin diagram we shall mean a list of 5 vector spaces P, E1, E2, E3, E4 over an algebraically closed field K, and 4 linear maps a1, a2, a3, a4 as shown.The spaces need not be of finite dimension.In their solution of the 4-subspace problem [6], Gelfand and Ponomarev have classified such representations when the spaces are finite dimensional. A representation like (1) can also be viewed as a module over the K-algebra R4 consisting of all 5 × 5 matrices having zeros off the first row and off the main diagonal.
Graphs with near v- and e-neighbourhoods
Authors: Fronček Dalibor 
Published: May 2009

All the graphs considered in this paper are connected finite undirected graphs without loops and multiple edges.By thevertex-neighbourhood (v-neighbourhood)of any vertexxin the graphGwe mean the subgraphinduced by the set of all vertices adjacent tox. Analogously by the edge-neighbourhood (e-neighbourhood) of any edgefwith end verticesx, ywe mean the subgraph(f) (or(xy)) induced by the set of all vertices which are adjacent to at least one vertex of the pair x, y and which are different fromx, y.
The normalizer of Γ0(N) in PSL(2, ℝ)
Authors: Akbas M. , Singerman D. 
Published: May 2009

Let Γ denote the modular group, consisting of the Möbius transformationsAs usual we denote the above transformation by the matrix remembering that V and – V represent the same transformation. If N is a positive integer we let Γ0(N) denote the transformations for which c ≡ 0 mod N. Then Γ0(N) is a subgroup of indexthe product being taken over all prime divisors of N.
Principally ordered regular semigroups
Authors: Blyth T. S. , Pinto G. A. 
Published: May 2009

An ordered semigroup S will be called principally ordered if, for every x ɛ S, there existsx* = max {y ɛ S; xyx ≤ x}.Here we shall be concerned with the case where S is regular. We begin by listing some basic properties that arise from the above definition. As usual, we shall denote by V(x) the set of inverses of x ɛ S.
Pairs of quadratic forms modulo one
Authors: Baker R. C. , Brüdern J. 
Published: May 2009

Let s be a natural number, s ≥ 2. We seek a positive number λ(s) with the following property:Let ε > 0. Let Q1(x1, …, xs), Q2(x1, …, xs) be real quadratic forms, then for N > C1(s, ε) we havefor some integers n1, …, ns,
Covering a group with isolators of finitely many subgroups
Authors: Longobardi Patrizia , Maj Mercede , Rhemtulla Akbar H. 
Published: May 2009

In [6] B. H. Neumann proved the following beautiful result:if a group G is covered by finitely many cosets, say G=xiHi, then we can omit from the union any xiHi, for which|G|Hj|is infinite. In particular, |G:Hj|is finite, for some j∈ {l,…,n}.In an unpublished result R. Baer characterized the groups covered by finitely many abelian subgroups, they are exactly the centre-by-finite groups [8]. Coverings by nilpotent subgroups or by Engel subgroups and by normal subgroups have been studied, for example, by R. Baer (see [8]), L. C. Kappe [2,1], M. A. Brodie and R. F. Chamberlain [1], and recently by M. J. Tomkinson [9].
Almost-Dedekind rings
Authors: Johnson E. W. 
Published: May 2009

Throughout we assume all rings are commutative with identity. We denote the lattice of ideals of a ringRbyL(R), and we denote byL(R)* the subposetL(R)−R.A classical result of commutative ring theory is the characterization of a Dedekind domain as an integral domainRin which every element ofL(R)* is a product of prime ideals (see Mori [5] for a history). This result has been generalized in a number of ways. In particular, rings which are not necessarily domains but which otherwise satisfy the hypotheses (i.e. general ZPI-rings) have been widely studied (see, for example, Gilmer [3]), as have rings in which only the principal ideals are assumed to satisfy the hypothesis (i.e. π-rings).
Linearization of holomorphic mappings on fully nuclear spaces with a basis
Authors: Dineen Seán , Galindo Pablo , García Domingo , Maestre Manuel 
Published: May 2009

In [13] Mazet proved the following result.If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].
The structure of discontinuous homomorphisms from non-commutative C*-algebras
Authors: Runde Volker 
Published: May 2009

LetXbe a compact Hausdorff space, letC(X)denote the algebra of all continuous functions onX, letBbe a Banach algebra, and let θ: →C(X)→Bbe a (possibly discontinuous) homomorphism with dense range. A classical theorem by W. G. Bade and P. C. Curtis ([2, Theorem 4.3]) describes in great detail the structure of θ we shall refer to this result as the Bade–Curtis theorem. Before we give a brief sketch of this theorem, we fix some notation. ForY⊂XletI(Y)andJ(Y)denote the ideals of all functions inC(X)that vanish onYand on a neighborhood ofYrespectively; ifY= {x} for somexɛX, we write mxandJxforI(Y)andJ(Y)respectively. According to the Bade–Curtis theorem there is a finite set {x1,…, xn) ⊂X, the so-calledsingularity setof θ, such that θ | ({x1, …, xn}) is continuous. As a consequence, the restriction of θ to the dense subalgebra ofC (X)consisting of all those functions which are constant near eachXj(j= 1,…,n) is continuous, and extends to a continuous homomorphism θcont:C(X)→B. Let θsing: = θ – θcont. Then θsing|I({x1,…, xn}) is a homomorphism onto a dense subalgebra of rad (B). θcont, and θsingare called thecontinuousand thesingular partof θ respectively. Moreover, there are linear maps:C(X)⊒Bsuch that(i)(ii)is a homomorphism, andCondition (iii) forces the homomorphismsto map into rad(B); such homomorphisms are calledradical homomorphisms.
On stationary phase integrals
Authors: Huxley M. N. 
Published: May 2009

Let f(x) and g(x) be real functions defined on the interval [a, b], with f(x) at least twice continuously differentiable, f′(x) monotone increasing, and f(x) of bounded variation. We consider the exponential integralwhere e(t) denotes exp 2πit. The purpose of this note is to prove sharp forms of the well-known estimates:A: If f′(x) is nonzero on [a, b], then I has order of magnitudeThe constant of proportionality depends on the function g(x).B: If f′(x) changes sign at x = c with a < c < b, then
Finite co-Dedekindian groups
Authors: Deaconescu Marian , Silberberg Gheorghe 
Published: May 2009

A group G is called Dedekindian if every subgroup ofG is normal in G.The structure of the finite Dedekindian groups is well-known [3, Satz 7.12]. They are either abelian or direct products of the form Q × A × B, where Q is the quaternion group of order 8, Ais abelian of odd order and exp(B) ≤ 2.
Automatic continuity of certain isomorphisms between regular Banach function algebras
Authors: Font Juan J. 
Published: May 2009

AbstractLetAandBbe regular semisimple commutative Banach algebras; that is to say, regular Banach function algebras. A linear mapTdenned fromAintoBis said to beseparatingordisjointness preservingiff.g = 0 impliesTf.Tg= 0, for allf, g∈ A In this paper we prove that ifAsatisfies Ditkin's condition then a separating bijection isautomatically continuousand its inverse is separating. If alsoBsatisfies Ditkin's condition, then it induces a homeomorphism between the structure spaces ofAandB.
Annihilators and the CS-condition
Authors: Nicholson W. K. , Yousif M. F. 
Published: May 2009

AbstractIt is proved that if every cyclic right R-module is torsionless and R is a left CS-ring then R is semiperfect left continuous with soc(RR)essential in RR. As a consequence every right cogenerator, left CS-ring R is shown to be right pseudo-Frobenius and left continuous, and an example is given to show that R need not be left selfinjective. It is also proved that if R is a left CS-ring and every cyclic right R-module embeds in a free module, then R is quasi-Frobenius if and only if J(R) ⊆ Z(RR).