Groups with Finitely Many Isomorphism Classes of Non-Normal Subgroups

Abstract

We study groups in which the non-normal subgroups fall into finitely many isomorphism classes. We prove that a locally generalized radical group with this property is abelian-by-finite and minimax. Here a generalized radical group is a group with an ascending series whose factors are either locally nilpotent or locally finite. We give also a complete description of locally finite groups with finitely many classes of non-normal subgroups.

Keywords

• isomorphism type
• normal subgroup
• radical group