Groups with the maximum condition on non-nilpotent subgroups (Q2705012)

This review also concerns the preceding item Zbl 0972.20019.NEWLINENEWLINENEWLINEThe second article deals with locally soluble-by-finite, non-locally-nilpotent groups. In the non-nilpotent but locally nilpotent case of a group \(G\) satisfying this condition with finite residual \(G^F\) there is the alternative (i) \(G/G^F\) is not finitely generated, \(G\) possesses a normal nilpotent subgroup \(U\) such that \(G/U\) is a Prüfer \(p\)-group and every nonnilpotent subgroup of \(G\) is supplement of \(U\) in \(G\); or (ii) \(G/G^F\) is finitely generated and \(G^F\) is a nilpotent and divisible Chernikov subgroup which is antinilpotent; or (iii) \(G/G^F\) is finitely generated and \(G\) is non-minimax and \(G^F\) is periodic and has no subgroups of finite index. (Theorems A, B, C).NEWLINENEWLINENEWLINEIf \(G\) is not locally nilpotent but locally soluble-by-finite, then \(G\) is finitely generated and an extension of its Hirsch-Plotkin radical \(L\) by an Abelian-by-finite group \(G/L\). The authors give more detailed information both on \(L\) and \(G/L\).