FC-nilpotent and FC-soluble groups

Abstract

Let an element of a group be called an FC element if it has only a finite number of conjugates in the group. Baer(1) and Neumann (8) have discussed groups in which every element is FC, and called them FC- groups . Both Abelian and finite groups are trivially FC-groups; Neumann has studied the properties common to FC-groups and Abelian groups, and Baer the properties common to FC-groups and finite groups. Baer has also shown that, for an arbitrary group G , the set H 1 of all FC elements is a characteristic subgroup. Haimo (3) has defined the FC- chain of a group G by H i / H i −1 is the subgroup of all FC elements in G / H i −1 .