Mutually Permutable Products of Finite Groups, II

On W -S-permutable Subgroups of Finite Groups∗

A subgroup H of a finite group G is said to be W -S-permutable in G if there is a subgroup K of G such that G = HK and H ∩K is a nearly S-permutable subgroup of G. In this article, we analyse the structure of a finite group G by using the properties of W -S-permutable subgroups and obtain some new characterizations of finite p-nilpotent groups and finite supersolvable groups. Some known results...

COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS

Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...

Automorphisms of direct products of finite groups II

In this paper we first find the automorphism group of the direct product of n copies of an indecomposable non-abelian group. We describe the automorphism group as matrices with entries which are homomorphisms between the n direct factors. We then use this description with a generalization of a result by Bidwell, Curran, and McCaughan on Aut (H×K), where H and K have no common direct factor, to ...

II. Products of Groups

Bicrossed Products for Finite Groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one be...