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Soluble groups isomorphic to their non-nilpotent subgroups. (English) Zbl 0943.20031
The authors characterize the groups of the title that are not finitely generated. Torsion-free groups in this class are nilpotent, those of infinite rank are Fitting groups, in case of finite rank the group is a certain extension of an Abelian divisible $$p$$-group by a cyclic group. Finitely generated groups of the title were characterized by the authors [see Glasg. Math. J. 40, No. 2, 257-262 (1998; Zbl 0908.20032)].

##### MSC:
 20F16 Solvable groups, supersolvable groups