A Transfer Theorem for Small Primes.
A variation of Thompson's conjecture for the symmetric groups
Let be a finite group and let denote the set of conjugacy class sizes of . Thompson’s conjecture states that if is a centerless group and is a non-abelian simple group satisfying , then . In this paper, we investigate a variation of this conjecture for some symmetric groups under a weaker assumption. In particular, it is shown that if and only if and has a special conjugacy class of size , where is a prime number. Consequently, if is a centerless group with , then .
A -theorem for -injectors in finite groups
Abelian Normal Subgroups of M-Groups.
Abelian quasinormal subgroups of groups
Let be any group and let be an abelian quasinormal subgroup of . If is any positive integer, either odd or divisible by , then we prove that the subgroup is also quasinormal in .
About ambivalent groups
About noncommuting graphs.
About the finite groups whose minimal normal subgroups are union of two conjugacy classes exactly
Active sums I.
Given a generating family F of subgroups of a group G closed under conjugation and with partial order compatible with inclusion, a new group S can be constructed, taking into account the multiplication in the subgroups and their mutual actions given by conjugation. The group S is called the active sum of F, has G as a homomorph and is such that S/Z(S) ≅ G/Z(G) where Z denotes the center.The basic question we investigate in this paper is: when is the active sum S of the family F isomorphic to the...
Active sums of groups.
Addendum and corrigendum to «Automorfismi che fissano i centralizzanti di un gruppo»
Addendum to : “Prime graph components of finite almost simple groups” [Rend. Sem. Mat. Univ. Padova 102 (1999), 1–22]
Adjoining conjugating elements to finite groups
Affinitäten endlicher Gruppen.
Algebre di Lie graduate in caratteristica due
Algorithms for permutability in finite groups
In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.
All geometries of the Mathieu group based on maximal subgroups.
Alternating group coverings of the affine line for characteristic greater than two.
An algorithm for the word problem in extensions and the dependence of its complexity on the group representation
An Amalgam Related to M_11 and SP_4(3)