Results 21 to 30 of about 686,790 (292)
$p$-groups with maximal elementary abelian subgroups of rank $2$ [PDF]
, 2010 Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2.
Mazza, Nadia, Glauberman, George
core +4 more sources
A generalization of the Chermak--Delgado measure on subgroups and its associated lattice [PDF]
International Journal of Group Theory, 2023 We generalize the Chermak--Delgado measure of a subgroup of a finite group $G$, $\mu(H) = |H||C_{G}(H)|$, and its associated lattice of subgroups with maximal measure. We consider mappings $M$ of the lattice of all subgroups $\mathrm{Sub}(G)$ into itself
William Cocke +2 more
doaj +1 more source
Wielandt′s Theorem and Finite Groups with Every Non-nilpotent Maximal Subgroup with Prime Index
Journal of Harbin University of Science and Technology, 2023 In order to give a further study of the solvability of a finite group in which every non-nilpotent maximal subgroup has prime index, the methods of the proof by contradiction and the counterexample of the smallest order and a theorem of Wielandt on the ...
TIAN Yunfeng, SHI Jiangtao, LIU Wenjing
doaj +1 more source
On a Maximal Subgroup of the Affine General Linear Group of GL(6, 2) [PDF]
Advances in Group Theory and Applications, 2021 The affine general linear group 2^5:GL(5, 2) of GL(6, 2) has 6 conjugacy classes of maximal subgroups. The largest maximal subgroup is a group of the form 2^(1+8)_+ : GL(4, 2). In this paper we firstly determine the conjugacy classes of G using the coset
Ayoub B.M. Basheer, Jamshid Moori
doaj +1 more source
Maximal subgroups and PST-groups [PDF]
Open Mathematics, 2013 Abstract A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp.
Ballester-Bolinches, Adolfo +3 more
openaire +5 more sources
The maximal subgroups of the classical groups in dimension 13, 14 and 15 [PDF]
, 2015 One might easily argue that the Classification of Finite Simple Groups is one of the most important theorems of group theory. Given that any finite group can be deconstructed into its simple composition factors, it is of great importance to have a ...
Schröder, Anna Katharina
core +2 more sources
TORSION MAXIMAL SUBGROUPS OF GLn(D) [PDF]
Journal of Algebraic SystemsLet D be a division ring over its center F. LetGLn(D)be the general linear group over D. In this article we prove thatifGLn(D)contains a maximal torsion subgroup M then D = F,FpcharF = p > 0 and F is algebraic over its prime subeldwhen-ever one of the ...
Reza Fallah-Moghaddam
doaj +1 more source
Every group is a maximal subgroup of the free idempotent generated semigroup over a band [PDF]
, 2013 Given an arbitrary group G we construct a semigroup of idempotents (band) BG with the property that the free idempotent generated semigroup over BG has a maximal subgroup isomorphic to G. If G is finitely presented then BG is finite. This answers several
Ruskuc, Nik +6 more
core +1 more source
Counting maximal arithmetic subgroups [PDF]
Duke Mathematical Journal, 2007 We study the growth rate of the number of maximal arithmetic subgroups of bounded covolumes in a semisimple Lie group using an extension of the method developed by Borel and Prasad.
Belolipetsky, M. +2 more
openaire +3 more sources
Semi-Extraspecial Groups with an Abelian Subgroup of Maximal Possible Order [PDF]
Advances in Group Theory and Applications, 2018 Let p be a prime. A finite p-group G is defined to be semi-extraspecial if for every maximal subgroup N in Z(G) the quotient G/N is a an extraspecial group. In addition, we say that G is ultraspecial if G is semi-extraspecial and |G : G′| = |G′|^2.
Mark L. Lewis
doaj +1 more source