Large characteristic subgroups and abstract group classes. Issue 8 (2nd August 2020) - de Giovanni, Francesco; Trombetti, Marco
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 is F -characteristic if any group containing an -subgroup of finite index has also a characteristic subgroup of finite index that belongs to . Thus the class 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.