Research Article

Large characteristic subgroups and abstract group classes

Published in: Quaestiones Mathematicae
Volume 43 , issue 8 , 2020 , pages: 1159–1172

DOI: 10.2989/16073606.2019.1602087

Author(s): Francesco de Giovanni , Italy , Marco Trombetti , Italy

Keywords: Characteristic subgroup , F-characteristic group class , Characteristic subgroup , F-characteristic group class

Download full text Get new issue alerts

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.

« A question about higher order z-ideals in commutative rings

Lorentz spaces of vector measures and real interpolation of operators »