Groups of Heineken-Mohamed
The groups of the title are non-nilpotent groups all of whose proper subgroups are both nilpotent and subnormal, we abbreviate to H-M-groups. The author shows: (I) There are H-M \(p\)-groups with trivial centre and commutator subgroups abelian of infinite exponent (Theorem 2.3). Hartley gave examples with abelian commutator subgroups of finite exponent. (II) There are H-M \(p\)-groups with \(G'\) of derived length \(d\) for every \(d\) (Theorem 3.7). By considering multipliers Bruno and Phillips showed how to construct groups with \(G'\) of nilpotency class 2. By the exhibited constructions the collection of known such groups is widened considerably.
scientific article; zbMATH DE number 735326