Large characteristic subgroups and abstract group classes. Issue 8 (2nd August 2020)

• Record Type: Journal Article
• Authors: de Giovanni, Francesco; Trombetti, Marco
• Is Part Of: Quaestiones mathematicae. Volume 43:Issue 8(2020)
• Page Start: 1159
• Page End: 1172
• Publication Date: 2020-08-02
• Subjects: Characteristic subgroup -- F-characteristic group class; 20E07 -- 20F19; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2019.1602087
• Languages: English
• ISSNs: 1607-3606

Abstract

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.