Search results for "combinatoric"
showing 10 items of 1776 documents
On maximal subgroups of finite groups
1991
(1991). On maximal subgroups of finite groups. Communications in Algebra: Vol. 19, No. 8, pp. 2373-2394.
Local Finite Group Theory
1982
The word local is used in finite group-theory in relation to a fixed prime p; thus properties of p-subgroups or their normalisers, for example, are regarded as local. In the case of a soluble group, then, everything is local, but an insoluble group also has global aspects. Now the local behaviour influences the global, that is, there are theorems in which the hypothesis involves only p-subgroups and their normalisers, but the conclusion involves the whole group. This chapter is an introduction to theorems of this sort.
A characteristic subgroup and kernels of Brauer characters
2005
If G is finite group and P is a Sylow p-subgroup of G, we prove that there is a unique largest normal subgroup L of G such that L ⋂ P = L ⋂ NG (P). If G is p-solvable, then L is the intersection of the kernels of the irreducible Brauer characters of G of degree not divisible by p.
On $MC$-hypercentral triply factorized groups
2007
A group G is called triply factorized in the product of two subgroups A, B and a normal subgroup K of G ,i fG = AB = AK = BK. This decomposition of G has been studied by several authors, investigating on those properties which can be carried from A, B and K to G .I t is known that if A, B and K are FC-groups and K has restrictions on the rank, then G is again an FC-group. The present paper extends this result to wider classes of FC-groups. Mathematics Subject Classification: 20F24; 20F14
Some Characterisations of Soluble SST-Groups
2016
All groups considered in this paper are finite. A subgroup H of a group G is said to be SS-permutable or SS-quasinormal in G if H has a supplement K in G such that H permutes with every Sylow subgroup of K. Following [6], we call a group G an SST-group provided that SS-permutability is a transitive relation in G, that is, if A is an SS-permutable subgroup of B and B is an SS-permutable subgroup of G, then A is an SS-permutable subgroup of G. The main aim of this paper is to present several characterisations of soluble SST-groups.
Generalizations of the periodicity Theorem of Fine and Wilf
2005
We provide three generalizations to the two-dimensional case of the well known periodicity theorem by Fine and Wilf [4] for strings (the one-dimensional case). The first and the second generalizations can be further extended to hold in the more general setting of Cayley graphs of groups. Weak forms of two of our results have been developed for the design of efficient algorithms for two-dimensional pattern matching [2, 3, 6].
On the product of a nilpotent group and a group with non-trivial center
2007
Abstract It is proved that a finite group G = A B which is a product of a nilpotent subgroup A and a subgroup B with non-trivial center contains a non-trivial abelian normal subgroup.
p-Blocks relative to a character of a normal subgroup
2018
Abstract Let G be a finite group, let N ◃ G , and let θ ∈ Irr ( N ) be a G-invariant character. We fix a prime p, and we introduce a canonical partition of Irr ( G | θ ) relative to p. We call each member B θ of this partition a θ-block, and to each θ-block B θ we naturally associate a conjugacy class of p-subgroups of G / N , which we call the θ-defect groups of B θ . If N is trivial, then the θ-blocks are the Brauer p-blocks. Using θ-blocks, we can unify the Gluck–Wolf–Navarro–Tiep theorem and Brauer's Height Zero conjecture in a single statement, which, after work of B. Sambale, turns out to be equivalent to the Height Zero conjecture. We also prove that the k ( B ) -conjecture is true i…
On the product of a π-group and a π-decomposable group
2007
[EN] The main result in the paper states the following: Let π be a set of odd primes. Let the finite group G=AB be the product of a π -decomposable subgroup A=Oπ(A)×Oπ′(A) and a π -subgroup B . Then Oπ(A)⩽Oπ(G); equivalently the group G possesses Hall π -subgroups. In this case Oπ(A)B is a Hall π-subgroup of G. This result extends previous results of Berkovich (1966), Rowley (1977), Arad and Chillag (1981) and Kazarin (1980) where stronger hypotheses on the factors A and B of the group G were being considered. The results under consideration in the paper provide in particular criteria for the existence of non-trivial soluble normal subgroups for a factorized group G.
On finite groups generated by strongly cosubnormal subgroups
2003
[EN] Two subgroups A and B of a group G are cosubnormal if A and B are subnormal in their join and are strongly cosubnormal if every subgroup of A is cosubnormal with every subgroup of B. We find necessary and sufficient conditions for A and B to be strongly cosubnormal in and, if Z is the hypercentre of G=, we show that A and B are strongly cosubnormal if and only if G/Z is the direct product of AZ/Z and BZ/Z. We also show that projectors and residuals for certain formations can easily be constructed in such a group. Two subgroups A and B of a group G are N-connected if every cyclic subgroup of A is cosubnormal with every cyclic subgroup of B (N denotes the class of nilpotent groups). Thou…