Soluble groups isomorphic to their non-nilpotent subgroups. (English) Zbl 0943.20031

Smith, Howard; Wiegold, James

J. Aust. Math. Soc., Ser. A 67, No. 3, 399-411 (1999).

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)].

Reviewer: H.Heineken (Würzburg)

MSC:

20F16

Solvable groups, supersolvable groups

Keywords:

soluble groups; isomorphisms with non-nilpotent subgroups; torsion-free groups; finitely generated groups; Fitting groups