Groups with the maximal condition (Q1311095)

The author proves that a group \(G\) with the maximal condition on subgroups satisfies one and only one of the following conditions: (a) \(G\) is nilpotent, (b) \(G\) has a finite soluble non-nilpotent section, (c) \(G\) is not nilpotent and, if \(H/K\) is a non-nilpotent section of \(G\) with \(K\) maximal with respect to this condition, every maximal nilpotent subgroup of \(H/K\) is self-normalizing and any two distinct maximal nilpotent subgroups of \(H/K\) have trivial intersection. As corollaries, the author obtains two sufficient conditions for a group with the maximal condition on subgroups to be nilpotent.