-systems of finite simple groups
Term functions on non-Abelian groups of order
The 27-dimensional module for E6. I.
The Alperin-McKay conjecture holds in the covering groups of symmetric and alternating groups, p ... 2.
The Artin exponent of finite groups
The automorphism group of a p-group of maximal class with an abelian maximal subgroup
The basic construction from the conditional expectation on the quantum double of a finite group
Let be a finite group and a subgroup. Denote by (or ) the crossed product of and (or ) with respect to the adjoint action of the latter on the former. Consider the algebra generated by and , where we regard as an idempotent operator on for a certain conditional expectation of onto . Let us call the basic construction from the conditional expectation . The paper constructs a crossed product algebra , and proves that there is an algebra isomorphism between and .
The Birkhoff-Neumann Embedding of Relatively Free Groups
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.