Delizia, Constantino; Rhemtulla, Akbar; Smith, Howard Locally graded groups with a nilpotency condition on infinite subsets. (English) Zbl 0982.20019 J. Aust. Math. Soc., Ser. A 69, No. 3, 415-420 (2000). A group is called locally graded if each non-trivial finitely generated subgroup has a non-trivial finite quotient. Here the authors study locally graded groups in the class \(N(2,k)^*\): this is the class of groups in which every infinite subset contains a pair of elements generating a nilpotent subgroup of class at most \(k\).The main result of the paper is: Theorem 1. Let \(G\) be a finitely generated, locally graded group in the class \(N(2,k)^*\). Then \(G/Z_c(G)\) is finite for some \(c=c(k)>0\). Reviewer: Derek J.S.Robinson (Urbana) Cited in 3 Documents MSC: 20F19 Generalizations of solvable and nilpotent groups 20E26 Residual properties and generalizations; residually finite groups 20E25 Local properties of groups 20F05 Generators, relations, and presentations of groups 20F14 Derived series, central series, and generalizations for groups Keywords:locally graded groups; nilpotent groups; finitely generated subgroups; finite quotient groups; central series PDFBibTeX XMLCite \textit{C. Delizia} et al., J. Aust. Math. Soc., Ser. A 69, No. 3, 415--420 (2000; Zbl 0982.20019) Full Text: DOI