Research Article

Large characteristic subgroups and abstract group classes

Published in: Quaestiones Mathematicae
Volume 43 , issue 8, 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,

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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.

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Research Article

Large characteristic subgroups and abstract group classes

Abstract

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