Groups whose proper subgroups are finite-by-nilpotent
The author considers non-finite-by-nilpotent groups with all proper subgroups finite-by-nilpotent; in short MNFN-groups. Finitely generated MNFN-groups \(G\) are perfect, with \(G/\Phi(G)\) infinite simple (Theorem 2.6); infinitely generated MNFN-groups belong to one of the following classes: (a) non-perfect MNFA-groups, (b) non-perfect MNN-groups with every subgroup subnormal, (c) locally nilpotent perfect MNN-groups (Theorem 3.5).
scientific article; zbMATH DE number 938546
scientific article