A classification of the finite non-solvable minimal non-CA-groups

Abstract

A group is called a CA-group if the centralizer of every non-central element is abelian. Furthermore, a group is called a minimal non- CA-group if it is not a CA-group itself, but all of its proper subgroups are. In this paper, we give a classification of the finite non-solvable minimal non- CA-groups.

On some second maximal subgroups of non-solvable groups

“…It is an important trend to extend the study of solvable groups to non-solvable groups, which has attracted the attention of many researchers( [3], [9]). In this paper, some characterizations for a non-solvable group are obtained by using properties of the second maximal subgroups which are related to non-c p -normal maximal subgroups.…”