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Papers by erzsebet horvath

In this paper we investigate general properties of Cartan invariants of a finite group G in chara... more In this paper we investigate general properties of Cartan invariants of a finite group G in characteristic 2. One of our results shows that the Cartan matrix of G in characteristic 2 contains an odd diagonal entry if and only if G contains a real element of 2-defect zero. We also apply these results to 2-blocks of symmetric groups and to blocks with normal or abelian defect groups. The second part of the paper deals with annihilators of certain ideals in centers of group algebras and blocks.

Journal of Algebra, 2001

Block induction is a correspondence between certain p-blocks of subgroups and blocks of the whole... more Block induction is a correspondence between certain p-blocks of subgroups and blocks of the whole group. It is a tool with the help of which one often can reduce the solution of problems in the whole group to smaller groups. The literature lists Ž several ways to define induced blocks in the sense of Brauer, Alperin and Burry,. Green, and Wheeler. It is well-known that any two of these concepts of block induction coincide in their common domain of definition; for example, each of Ž. Ž. them is defined if the subgroup H of the group G satisfies DC D F H F N D , G G for a p-subgroup D of G. We study some other features of blocks which are compatible with the above induction concepts in this sense, and formulate them as induction concepts so that one could deal with these and the above concepts in a unified way. We compare their fields of definition to the others in general and in the special cases of defect zero blocks and of p-groups. We give some sufficient conditions so that induction would not be defined in any sense. We show that, unlike in the case of Brauer sense induction, block induction in the sense of Alperin-Burry is not always defined from the normalizer of a chain of p-subgroups. Our example also shows that ''admissible induction'' and ''being of multiplicity one'' are not transitive. In the last part of the paper, we study the connection of the defect groups of the induced and the original block, in the case where the latter group is abelian.

Archiv der Mathematik, 2006

ABSTRACT . It was initiated by the second author to investigate in which groups the left and righ... more ABSTRACT . It was initiated by the second author to investigate in which groups the left and right stabilizers of subsets have equal order. First we prove that if the left and right stabilizers of sets of prime power size are equal order then the group is supersolvable. We also characterize those 2-groups which satisfy this property for p = 2. We show that if in a finite group, the left and right stabilizers of sets of prime power size have equal order, then the commutator subgroup is abelian. Finally we characterize hamiltonian groups with the help of one-sided stabilizers.

Osaka Journal of Mathematics, 2011

We consider real versions of Brauer’s k(B) conjecture, Olsson’s conjecture and Eaton’s conjecture... more We consider real versions of Brauer’s k(B) conjecture, Olsson’s conjecture and Eaton’s conjecture. We prove the real version of Eaton’s conjecture for 2-blocks of groups with cyclic defect group and for the principal 2-blocks of groups with trivial real core. We also characterize G-classes, real and rational G-classes of the defect group ofB.

arXiv: Group Theory, 2019

We show that for each positive integer nnn, there are a group GGG and a subgroup HHH such that th... more We show that for each positive integer nnn, there are a group GGG and a subgroup HHH such that the ordinary depth is d(H,G)=2nd(H, G) = 2nd(H,G)=2n. This solves the open problem posed by Lars Kadison whether even ordinary depth larger than 666 can occur.

The Sylow p-subgroups of the symmetric group S_p^n satisfy the appropriate generalization of Masc... more The Sylow p-subgroups of the symmetric group S_p^n satisfy the appropriate generalization of Maschke's Theorem to the case of a p'-group acting on a (not necessarily abelian) p-group. Moreover, some known results about the Sylow p-subgroups of S_p^n are stated in a form that is true for all primes p.

Proceedings of the Edinburgh Mathematical Society, 2011

Let G be a finite group, let p be a prime divisor of the order of G and let k(G) be the number of... more Let G be a finite group, let p be a prime divisor of the order of G and let k(G) be the number of conjugacy classes of G. By disregarding at most finitely many non-solvable p-solvable groups G, we have k(G)geq2smashsqrtp−1k(G)\geq2\smash{\sqrt{p-1}}k(G)geq2smashsqrtp−1 with equality if and only if if smashsqrtp−1\smash{\sqrt{p-1}}smashsqrtp−1 is an integer, G=CprtimessmashCsqrtp−1G=C_{p}\rtimes\smash{C_{\sqrt{p-1}}}G=CprtimessmashCsqrtp−1 and CG(Cp) = Cp. This extends earlier work of Héthelyi, Külshammer, Malle and Keller.

Journal of Algebra, 2005

In this paper, we investigate certain ideals in the center of a symmetric algebra A over an algeb... more In this paper, we investigate certain ideals in the center of a symmetric algebra A over an algebraically closed field of characteristic p > 0. These ideals include the Higman ideal and the Reynolds ideal. They are closely related to the p-power map on A. We generalize some results concerning these ideals from group algebras to symmetric algebras, and we obtain some new results as well. In case p = 2, these ideals detect odd diagonal entries in the Cartan matrix of A. In a sequel to this paper, we will apply our results to group algebras.

Journal of Algebra, 2006

Journal of Algebra, 2004

We prove a generalization of the Brauer-Nesbitt theorem. We study the Robinson map and relations ... more We prove a generalization of the Brauer-Nesbitt theorem. We study the Robinson map and relations between p-regular conjugacy classes and block idempotents with common defect group. We characterize defect classes and those class sums whose images under the Brauer map are not nilpotent.

Journal of Algebra, 2008

We consider Galois actions on blocks and conjugacy classes. We extend some of the results valid i... more We consider Galois actions on blocks and conjugacy classes. We extend some of the results valid in the case of complex conjugation. We give some counterexamples where this extension is not possible.

Communications in Algebra, 2015

We determine the combinatorial depth of certain subgroups of simple Suzuki groups Sz(q), among ot... more We determine the combinatorial depth of certain subgroups of simple Suzuki groups Sz(q), among others, the depth of their maximal subgroups. We apply these results to determine the ordinary depth of these subgroups.

Archiv der Mathematik, 1996

In t950 L. R6dei proved in [4] that A5 is the unique simple group of even order which is non-abel... more In t950 L. R6dei proved in [4] that A5 is the unique simple group of even order which is non-abelian but each of its non-maximal proper subgroup is abelian. Seven years later M. Suzuki observed in [5] that this characterization of A5 remains valid if we take nilpotency in place of abelity. The present note contains an even stronger characterization of A s. This is formulated in Theorem 1.2 below.

So far there has been elementary proof for Frobenius&#x27;s theorem only in special cases... more So far there has been elementary proof for Frobenius&#x27;s theorem only in special cases: if the complement is solvable, see e.g. [3], if the complement is of even order, see e.g. [6]. In the first section we consider the case, when the order of the complement is odd. We define a graph the vertices of which are the set K