Search results for "Finite group"
showing 10 items of 205 documents
Characters and Blocks of Finite Groups
1998
This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Fi…
Groups with exactly one irreducible character of degree divisible byp
2014
Let [math] be a prime. We characterize those finite groups which have precisely one irreducible character of degree divisible by [math] .
Blocks with 𝑝-power character degrees
2005
Let B B be a p p -block of a finite group G G . If χ ( 1 ) \chi (1) is a p p -power for all χ ∈ Irr ( B ) \chi \in \operatorname {Irr}(B) , then B B is nilpotent.
Nondivisibility among character degrees II: Nonsolvable groups
2007
We say that a finite group G is an NDAD-group (no divisibility among degrees) if for any 1 < a < b in the set of degrees of the complex irreducible characters of G, a does not divide b. In this article, we determine the nonsolvable NDAD-groups. Together with the work of Lewis, Moreto and Wolf (J. Group Theory 8 (2005)), this settles a problem raised by Berkovich and Zhmud’, which asks for a classification of the NDAD-groups.
Confined subgroups in periodic simple finitary linear groups
2002
A subgroupX of the locally finite groupG is said to beconfined, if there exists a finite subgroupF≤G such thatX g∩F≠1 for allg∈G. Since there seems to be a certain correspondence between proper confined subgroups inG and non-trivial ideals in the complex group algebra ℂG, we determine the confined subgroups of periodic simple finitary linear groups in this paper.
Multiply Transitive Permutation Groups
1982
Since the beginnings of finite group theory, the multiply transitive permutation groups have exercised a certain fascination. This is mainly due to the fact that apart from the symmetric and alternating groups not many of them were known. Only very recently final results about multiply transitive permutation groups have been proved, using the classification of all finite simple groups (see 7.5).
On groups having a p-constant character
2020
Let G G be a finite group, and p p a prime number; a character of G G is called p p -constant if it takes a constant value on all the elements of G G whose order is divisible by p p . This is a generalization of the very important concept of characters of p p -defect zero. In this paper, we characterize the finite p p -solvable groups having a faithful irreducible character that is p p -constant and not of p p -defect zero, and we will show that a non- p p -solvable group with this property is an almost-simple group.
Products of formations of finite groups
2006
[EN] In this paper criteria for a product of formations to be X-local, X a class of simple groups, are obtained. Some classical results on products of saturated formations appear as particular cases.
On X-saturated formations of finite groups
2005
[EN] In the paper, a Frattini-like subgroup associated with a class X of simple groups is introduced and analysed. The corresponding X-saturated formations are exactly the X-local ones introduced by Förster. Our techniques are also very useful to highlight the properties and behaviour of omega-local formations. In fact, extensions and improvements of several results of Shemetkov are natural consequences of our study.
On a class of supersoluble groups
2014
A subgroup H of a finite group G is said to be S-semipermutable in G if H permutes with every Sylow q-subgroup of G for all primes q not dividing |H|. A finite group G is an MS-group if the maximal subgroups of all the Sylow subgroups of G are S-semipermutable in G. The aim of the present paper is to characterise the finite MS-groups.