singular continuous spectrum for palindromic schrodinger operators we give new examples of discrete schrodinger operators with potentials taking finitely many values that have purely singular continuous spectrum if the hullx of the potential is strictly ergodic then the existence of just one potentialx inx for which the operator has no eigenvalues implies that there is a generic set inx for which the operator has purely singular continuous spectrum a sufficient condition for the existence of such anx is that there is az x that contains arbitrarily long palindromes thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset inx the class includes well known substitutions like fibonacci thue morse period doubling binary non pisot and ternary non pisot we also show that the operator has no absolutely continuous spectrum for allx x ifx derives from a primitive substitution for potentials defined by circle maps x n 1 j 0 n we show that the operator has purely singular continuous spectrum for a generic subset inx for all irrational and every half open intervalj

abelian sylow subgroups in a finite group ii abstract let p 3 5 be a prime we prove that sylow p subgroups of a finite group g are abelian if and only if the class sizes of the p elements of g are all coprime to p this gives a solution to a problem posed by r brauer in 1956 for p 3 5

palindromic length of words and morphisms in class p abstract we study the palindromic length of factors of infinite words fixed by morphisms of the so called class p introduced by hof knill and simon we show that it grows at most logarithmically with the length of the factor for the fibonacci word and the thue morse word we provide explicit bounds on their rate of growth we also construct an infinite word rich in palindromes for which the palindromic length grows as n

brauer s height conjecture for p solvable groups we complete the proof of the height conjecture for p solvable groups using the classification of finite simple groups introduction the height conjecture is the statement that a p block of a finite group has an abelian defect group if and only if all ordinary irreducible characters in the block have height zero while a proof of this conjecture for general finite groups seems remote considerable progress has been made toward proving it for p solvable groups fong 5 proved that all characters in a block with abelian defect group have height zero in a p solvable group and he proved the converse direction for the principal block 5 and for solvable groups in the case that p is the largest prime divisor of the group order 6 recently 24 8 the converse direction has been established for all solvable groups in this paper we prove the converse direction for all p solvable groups assuming the classification of finite simple groups in its general outline this paper resembles 8 where we proved the height conjecture for solvable groups the reader is assumed to have some familiarity with 8 now we state our main results the analogs of the main results of 8 theorem a suppose that n g that g n is p solvable that t e irr n and that p 1 x i w l for all x e irr g i p then the p sylow subgroups of g n are abelian theorem b let b be a p block of a p solvable group with defect group d if every ordinary irreducible character in b has height zero then d is abelian theorem c suppose that n g that g n is p solvable and that w e irr n suppose that e is an integer such that pe l does not divide x i w l for all x e irr g ip then the derived length of a p sylow subgroup of g n is at most 2e 1 theorem d let b and d be as in theorem b if every ordinary irreducible character in b has height at most e then the derived length of d is at most 2e 1 received by the editors january 10 1983 1980 mathematics subject classification primary 20c20 20c 15 1984 american mathematical society 0002 9947 84 1 00 25 per page

character tables and defect groups abstract let b be a block of a finite group g with defect group d we prove that the exponent of the center of d is determined by the character table of g in particular we show that d is cyclic if and only if b contains a large family of irreducible p conjugate characters more generally for abelian d we obtain an explicit formula for the exponent of d in terms of character values in small cases even the isomorphism type of d is determined in this situation moreover it can read off from the character table whether d d 4 where d denotes the commutator subgroup of d we also propose a new characterization of nilpotent blocks in terms of the character table

large time asymptotics in contaminant transport in porous media in this paper we derive large time solutions of the partial differential equations modelling contaminant transport in porous media for initial data with bounded support while the main emphasis is on two space dimensions for the sake of completeness we give a brief summary of the corresponding results for one space dimension the philosophy behind the paper is to compare the results of a formal asymptotic analysis of the governing equations as t to infty with numerical solutions of the complete initial value problem the analytic results are obtained using the method of dominant balance which identifies the dominant terms in the model equations determining the behaviour of the solution in the large time limit these are found in terms of time scaled space similarity variables and the procedure results in a reduction of the number of independent variables in the original partial differential equation this generates what we call a reduced equation the solution of which depends crucially on the value

characters of relative p degree over normal subgroups let z be a normal subgroup of a finite group g let irr z be an irreducible complex character of z and let p be a prime number if p does not divide the integers 1 1 for all irr g lying over then we prove that the sylow p subgroups of g z are abelian this theorem which generalizes the gluck wolf theorem to arbitrary finite groups is one of the principal obstacles to proving the celebrated brauer height zero conjecture

time discretization schema for an integrodifferential sobolev type equation with integral conditions abstract the appropriate discretization in time schema is considered for approximating the solution of a nonlinear integro differential sobolev type equation with integral conditions we construct a discrete numerical solution of the discretized problem then some a priori estimates for the approximations are derived while the convergence of the method and the well posedness of the problem under study are established

on the conjugacy class of the fibonacci dynamical system we characterize the symbolical dynamical systems which are topologically isomorphic to the fibonacci dynamical system we prove that there are infinitely many injective primitive substitutions generating a dynamical system in the fibonacci conjugacy class in this class there are infinitely many dynamical systems not generated by a substitution an example is the system generated by doubling the 0 s in the infinite fibonacci word

partial functional differential equation with an integral condition and applications to population dynamics in this work we consider a semilinear functional partial differential equation with an integral condition we apply the method of semidiscretization in time to establish the existence and uniqueness of solutions we also study the continuation of the solution to the maximal interval of existence finally we give examples to demonstrate the applications of our results

p theory and modular representation theory in a previous paper 191 we observed a close relationship between the generalized core u g of a finite group g i e roughly speaking the core one has quite often to work with in pure group theory if one leaves the class of p solvable groups and the principal p block it turned out that o g with modifications for p 2 coincides with 0 g the group generated by the support of the centrally primitive idempotent f g corresponding to the principal p block this observation was the central point for a number of new results in modular representation theory which indicate that 0 g may be viewed as the generalized core in modular representation theory from this point of view it is worth paying more attention to this group thus the aim of this note is to polish the theory around o1 g and to see the connection with o g in a new light all groups under consideration are finite all modules finitely generated modules over some group algebra fg where f always denotes a field of characteristic p 0 the author wishes to thank the referee for many helpful suggestions concerning the revision of an earlier version of this paper

brauer s height zero conjecture for two primes let p and q be two primes we propose that brauer s height zero conjecture for the principal p blocks of finite groups can naturally be extended from the perspective of q we prove one direction of this new conjecture and show the reverse direction assuming that the inductive alperin mckay condition holds for the finite simple groups

solutions to rayleigh love equation with constant coefficients and delay forcing term abstract in this paper we applied the rothe time discretization method for establishing the sufficient conditions for the existence and uniqueness of a strong solution of a rayleigh love equation with constant coefficients and delay forcing term subject to history initial and integral conditions we also provided an example to illustrate the main result

solvability of a fractional boundary value problem with fractional integral condition abstract using banach contraction principle and leray schauder nonlinear alternative we establish sufficient conditions for the existence and uniqueness of solutions for boundary value problems for fractional differential equations with fractional integral condition involving the caputo fractional derivative some examples are given to illustrate our results

equivariant splendid rickard equivalences abstract broue s conjecture says that if a finite group h has an abelian sylow p subgroup p then the principal blocks of h and n h p are splendidly rickard equivalent in this paper broue s conjecture is reduced to simple groups with a stability condition a structure theorem on finite groups with abelian sylow p subgroups due to kimmerle and sandling is used

nilpotent and abelian hall subgroups in finite groups the research of the first second fourth fifth and sixth authors was supported by the prometeo generalitat valenciana proyectos mtm2010 15296 mtm2010 19938 c03 02 fundacio bancaixa p11b2010 47 and fondos feder the third author gratefully acknowledges financial support by erc advanced grant 291512 the seventh author was supported by the nsa grant h98230 13 1 0229 the eighth author gratefully acknowledges the support of the nsf grants dms 0901241 and dms 1201374

block separations and inclusions abstract we investigate the separation of characters by blocks at different primes and the inclusions of q blocks in p blocks viewed as sets of characters and use these notions to prove results on the structure of the corresponding groups in particular we provide a new criterion for the nilpotence of a finite group g based on the separation by principal blocks and we show that a condition on block unions has strong structural consequences

trivial intersection of blocks and nilpotent subgroups abstract let p q be different primes and suppose that the principal p and the principal q block of a finite group have only one irreducible complex character in common namely the trivial one we conjecture that this condition implies the existence of a nilpotent hall p q subgroup and prove that a minimal counter example must be an almost simple group where pq divides the order of its simple nonabelian normal subgroup as an immediate consequence we obtain that the conjecture holds true for p solvable or q solvable groups furthermore we prove the conjecture in case 2 p q using the classification theorem of finite simple groups finally we consider the situation that the intersection of an arbitrary p block with an arbitrary q block contains only one irreducible character

anderson localization for bernoulli and other singular potentials we prove exponential localization in the anderson model under very weak assumptions on the potential distribution in one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment in particular this solves the longstanding problem of localization for bernoulli potentials i e potentials that take only two values in dimensions greater than one we prove localization at high disorder for potentials with holder continuous distributions and for bounded potentials whose distribution is a convex combination of a holder continuous distribution with high disorder and an arbitrary distribution these include potentials with singular distributions we also show that for certain bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component

on the least number of palindromes contained in an infinite word we investigate the least number of palindromic factors in an infinite word we first consider general alphabets and give answers to this problem for periodic and non periodic words closed or not under reversal of factors we then investigate the same problem when the alphabet has size two

optimal approximation to a class of nonlinear evolution equations abstract in this paper we have developed and discussed a generalized difference method gdm for the approximation of a class of nonlinear evolution equations with integral items in one space dimension the main idea of the paper is to introduce a generalized volterra projection operator and we design a generalized difference formulation with a new approximate value of initial function which is of special importance for the error analysis then some theories of the generalized volterra projection operator are analyzed finally we deduce the optimal error estimates moreover some conclusions are obtained and our further research work is proposed

quasi isolated blocks and brauer s height zero conjecture this paper has two main results firstly we complete the parametrisation of all p blocks of nite quasi simple groups by nding the so called quasi isolated blocks of exceptional groups of lie type for bad primes this relies on the explicit decomposition of lusztig induction from suitable levi subgroups our second major result is the proof of one direction of brauer s long standing height zero conjecture on blocks of nite groups using the

on a time discretization method for a semilinear heat equation with purely integral conditions in a nonclassical function space abstract in this paper we construct a semidiscrete approximate solution to a semilinear one dimensional heat equation subject to integral boundary conditions by means of the rothe discretization in time method the convergence of the approximation scheme obtained is proved yielding the well posedness of the problem considered

sylow numbers and nilpotent hall subgroups let be a set of primes and g a finite group we characterize the existence of a nilpotent hall subgroup of g in terms of the number of sylow subgroups for the primes in

finite difference spectral approximations for the time fractional diffusion equation in this paper we consider the numerical resolution of a time fractional diffusion equation which is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order a with 0 a 1 the main purpose of this work is to construct and analyze stable and high order scheme to efficiently solve the time fractional diffusion equation the proposed method is based on a finite difference scheme in time and legendre spectral methods in space stability and convergence of the method are rigourously established we prove that the full discretization is unconditionally stable and the numerical solution converges to the exact one with order o dt 2 a n m where dt n and m are the time step size polynomial degree and regularity of the exact solution respectively numerical experiments are carried out to support the theoretical claims

solution to an integrodifferential equation with integral condition in this paper we are concerned with the application of rothe time discretization scheme to find an approximate solution of degenerate parabolic integrodifferential equation with initial neumann and nonlocal integral conditions existence and uniqueness of weak solution as well as some regularity results are obtained

rothe s method for an integrodifferential equation with integral conditions this work deals with an integrodifferential equation with initial newman and integral conditions the existence and uniqueness of the weak solution in an appropriate sense is proved by the method of rothe

the method of lines applied to nonlinear nonlocal functional differential equations this paper discusses nonlinear functional differential equation in a real reflexive banach space with nonlocal history condition by using the method of lines the existence and uniqueness of a strong solution are established finally some applications of the abstract results are presented

composition factors from the table of marks let b g be the burnside ring for a finite group g and let t g be the table of marks of g it is known that in general neither b g nor t g determines the finite group g that is one can easily construct pairs of non isomorphic finite groups such that their table of marks is the same hence their burnside rings are isomorphic in this note we show that the composition factors of g are determined by the table of marks t g

well posedness and spectral properties of heat and wave equations with non local conditions abstract we consider the one dimensional heat and wave equations but instead of boundary conditions we impose on the solution certain non local integral constraints an appropriate hilbert setting leads to an integration by parts formula in sobolev spaces of negative order and eventually allows us to use semigroup theory leading to analytic well posedness hence sharpening regularity results previously obtained by other authors in doing so we introduce a parametrization of such integral conditions that includes known cases but also shows the connection with more usual boundary conditions like periodic ones in the self adjoint case we even obtain eigenvalue asymptotics of so called weyl s type

on the number of classes of conjugate hall subgroups in finite simple groups abstract in this paper we find the number of classes of conjugate hall subgroups in all finite almost simple groups we also complete the classification of hall subgroups in finite simple groups and correct some mistakes from our previous paper

mirror substitutions and palindromic sequences by introducing the notion of mirror substitution we show that given a substitutive sequence over two letters it is palindromic that is it contains arbitrarily long palindromes if and only if its language is mirror invariant that is it is closed under the mirror image map then we solve a question of hof knill and simon in the 2 letter case and also by constructing a counterexample we give a negative answer to the open problem 4 in the webpage http iml univ mrs fr bernat openquestions html

confirmation for wielandt s conjecture abstract let be a set of primes by h wielandt s definition sylow theorem holds for a finite group g if all maximal subgroups of g are conjugate in the paper the following statement is proven assume that is a union of disjoint subsets and and a finite group g possesses a hall subgroup which is a direct product of a subgroup and a subgroup furthermore assume that both the sylow theorem and theorem hold for g then the sylow theorem holds for g this result confirms a conjecture posed by h wielandt in 1959

oscillation criteria for impulsive partial fractional differential equations in this paper we established some sufficient conditions for oscillation of solutions of a class of impulsive partial fractional differential equations with forcing term subject to robin and dirichlet boundary conditions by using differential inequality method as an application we included an example to illustrate the main result

a study of delayed cooperation diffusion system with dirichlet boundary conditions abstract in this paper we study the existence and uniqueness of strong solution of a delayed cooperation diffusion system with dirichlet boundary conditions using the method of semidiscretization in time

palindrome complexity we study the palindrome complexity of infinite sequences on finite alphabets i e the number of palindromic factors blocks of given length occurring in a given sequence we survey the known results and obtain new results for some sequences in particular for rote sequences and for fixed points of primitive morphisms of constant length belonging to class p of hof knill simon we also give an upper bound for the palindrome complexity of a sequence in terms of its block complexity

solution of nonlinear transport diffusion problems by linearization we construct and analyze a fully discretization scheme for approximating the solution of a class of nonlinear degenerate parabolic problems with a nonlinear neumann boundary conditions the method is based on rothe type discretization in time and on wavelet galerkin discretization in space a proof of convergence of the approximate solution is given and error estimates are proved

rothe s method for a telegraph equation with integral conditions abstract we study the existence and uniqueness of the solution for a telegraph equation with integral condition we apply the rothe time discretization method then we prove its convergence

rothe s method for solving some fractional integral diffusion equation abstract in this paper we apply the rothe s method to a fractional integral diffusion equation and establish the existence and uniqueness of a strong solution as an application we include an example to illustrate the main result

small intersections of principal blocks abstract in this note it is shown that a finite group g is solvable if for each odd prime divisor p of g irr b 0 g 2 irr b 0 g p 2 where irr b 0 g p is the set of complex irreducible characters of the principal p block b 0 g p of g also the structure of such groups is investigated examples show that the bound 2 is best possible