Abdollahi, Alireza; Taeri, Bijan A condition of finitely generated soluble groups. (English) Zbl 0942.20014 Commun. Algebra 27, No. 11, 5633-5638 (1999). In this note the authors prove that if \(G\) is a finitely generated soluble group, then every infinite subset of \(G\) contains two elements generating a nilpotent group of class \(\leq k\) if and only if \(G\) is an extension of a finite group by a group in which every 2-generator subgroup is nilpotent of class \(\leq k\). Reviewer: D.J.S.Robinson (Urbana) Cited in 1 ReviewCited in 8 Documents MSC: 20F16 Solvable groups, supersolvable groups 20F18 Nilpotent groups 20F05 Generators, relations, and presentations of groups Keywords:finitely generated soluble groups; nilpotent \(2\)-generator subgroups PDFBibTeX XMLCite \textit{A. Abdollahi} and \textit{B. Taeri}, Commun. Algebra 27, No. 11, 5633--5638 (1999; Zbl 0942.20014) Full Text: DOI References: [1] Delizia, C. 1994.Finitely Generated Soluble Groups with a Condition on Infinite Subsets, Vol. A128, 201–208. Instito Lombardo. Rend. Sc · Zbl 0882.20020 [2] DOI: 10.1080/00927879608825768 · Zbl 0878.20021 [3] DOI: 10.1017/S1446788700024253 [4] DOI: 10.1017/S1446788700019303 [5] DOI: 10.1017/S1446788700015469 · Zbl 0274.20033 [6] Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups (1972) · Zbl 0243.20032 [7] Robinson D.J.S., A Course in the Theory of Groups (1982) · Zbl 0483.20001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.