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      On finite-by-nilpotent groups

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          Abstract

          Let \(\gamma_n=[x_1,\dots,x_n]\) be the \(n\)th lower central word. Denote by \(X_n\) the set of \(\gamma_n\)-values in a group \(G\) and suppose that there is a number \(m\) such that \(|g^{X_n}|\leq m\) for each \(g\in G\). We prove that \(\gamma_{n+1}(G)\) has finite \((m,n)\)-bounded order. This generalizes the much celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite.

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          Most cited references7

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          Groups Covered By Permutable Subsets

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            Groups with Boundedly Finite Classes of Conjugate Elements

            J. Wiegold (1957)
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              An Essay on BFC Groups

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                Author and article information

                Journal
                03 July 2019
                Article
                1907.02798
                5fd8f7c2-1de3-4d4e-a7c6-e2f2b8d70e8e

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                20E45, 20F12, 20F24
                arXiv admin note: text overlap with arXiv:1803.04202
                math.GR

                Algebra
                Algebra

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