The Bogomolov multiplier of groups of order and exponent
We conduct an in-depth investigation into the structure of the Bogomolov multiplier for groups of order and exponent . We present a comprehensive...
The Characterisation of the Suzuki Groups by Their Sylow 2-Subgroups.
The classification of finite groups by using iteration digraphs
A digraph is associated with a finite group by utilizing the power map defined by for all , where is a fixed natural number. It is denoted by . In this paper, the generalized quaternion and -groups are studied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a -group are determined for a -group to be a generalized quaternion group. Further, the classification of two generated -groups as abelian or non-abelian...
The conjugacy classes in a finite simple group.
The conjugacy vector of a p-group of maximal class (I)
The conjugacy-vectors of all relative holomorphs of an elementary Abelian group of order 16
The Conway-Norton algebras for ?(6,3), ?(7,3), F'24, and their full automorphism groups.
The Core-Free Groups of Sylow-2-type M24.
The -property of linear and unitary groups.
The defect groups of a clique, p-solvable groups, and Alperin's conjecture.
The Derived Series of a Join of Subnormal Sugroups.
The determination of abelian Hall subgroups by a conjugacy class structure.
The object of this article is to show that a Jordan-Hölder class structure of a finite group determines abelian Hall subgroups of the group up to isomorphism. The proof uses this classification of the finite simple groups.
The diameter of the character degree graph..
The distribution of second -class groups on coclass graphs
General concepts and strategies are developed for identifying the isomorphism type of the second -class group , that is the Galois group of the second Hilbert -class field , of a number field , for a prime . The isomorphism type determines the position of on one of the coclass graphs , , in the sense of Eick, Leedham-Green, and Newman. It is shown that, for special types of the base field and of its -class group , the position of is restricted to certain admissible branches of coclass...
The Embedding of Quasinormal Subgroups in Finite Groups.
The Erdős-Ginzburg-Ziv theorem in Abelian non-cyclic groups.
The Erdős-Heilbronn problem for finite groups
The Euler class and periodicity of group cohomology.
The Factorisation of the Alternating and Symmetric Groups.
The Fitting Clas ...*.