Groups with restrictions on their infinite normal subgroups
This paper is concerned with classes of groups I\({\mathcal X}\) where \({\mathcal X}\) is the class of finite groups (\({\mathcal F})\) or abelian groups (\({\mathcal A})\) and a group is in I\({\mathcal X}\) if G is not in \({\mathcal X}\), but all quotients of G by an infinite normal subgroup are in \({\mathcal X}\). Radical- by-finite I\({\mathcal F}\) groups are fully characterized and the remaining I\({\mathcal F}\) groups are also described in some detail. Nilpotent I\({\mathcal A}\) groups are shown to exist in a variety of forms, with several characterizations being given. Finally soluble non-nilpotent I\({\mathcal A}\) groups are studied, again with satisfying results. A number of examples and constructions are given. The description of the various classes are not unduly technical.
Radical-by-finite I\({\mathcal F}\) groups
soluble non-nilpotent I\({\mathcal A}\) groups
scientific article; zbMATH DE number 4198321