Large characteristic subgroups and abstract group classes

Abstract

It is well-known that every virtually abelian group contains an abelian characteristic subgroup of finite index. We shall say that a group class X is F characteristic if any group containing an X-subgroup of finite index has also a characteristic subgroup of finite index that belongs to X. Thus the class A of abelian groups is F-characteristic. Many other relevant group classes have recently been proved to be F-characteristic, and the aim of this paper is to give a further contribution to this topic, in particular in the context of classes of generalized nilpotent groups.

Mathematics Subject Classification (2010): 20E07, 20F19.

Keywords: Characteristic subgroup, F-characteristic group class