A rank 3 tangent complex of , odd.
A remark on a Theorem of J. G. Thompson
An important theorem by J. G. Thompson says that a finite group is -nilpotent if the prime divides all degrees (larger than 1) of irreducible characters of . Unlike many other cases, this theorem does not allow a similar statement for conjugacy classes. For we construct solvable groups of arbitrary -lenght, in which the lenght of any conjugacy class of non central elements is divisible by .
A Remark on Blocks with Dihedral Defect Groups in Solvable Groups.
A remark on homogeneous sets in finite groups. (Eine Bemerkung über homogene Mengen in endlichen Gruppen.)
A remark on operating groups.
A result about cosets
A Root System for the Lyons Group.
A simple construction for the Fischer-Griess monster group.
A simple proof of Baer;s and Sato's theorems on lattice-isomorphisms between groups
A simple proof is given of a well-known result of the existance of lattice-isomorphisms between locally nilpotent quaternionfree modular groups and abelian groups.
A solvability criterion for finite groups related to character degrees
Let be a fixed positive integer. In this paper, we consider finite groups each of whose nonlinear character degrees has exactly prime divisors. We show that such groups are solvable whenever . Moreover, we prove that if is a non-solvable group with this property, then and is an extension of or by a solvable group.
A Theorem of Sylow Type for Finite Groups.
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...