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On profinite groups with word values covered by nilpotent subgroups

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Abstract

Let N stand for the class of nilpotent groups or one of its well-known generalizations. For a multilinear commutator word w and a profinite group G we show that w(G) is finite-by-N if and only if the set of wvalues in G is covered by countably many finite-by-N subgroups. Earlier this was known only in the case where w = x or w = [x, y].

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121, Padova, Italy

    Eloisa Detomi

  2. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126, Bologna, Italy

    Marta Morigi

  3. Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900, Brazil

    Pavel Shumyatsky

Authors
  1. Eloisa Detomi
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  2. Marta Morigi
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  3. Pavel Shumyatsky
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Correspondence to Eloisa Detomi.

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Detomi, E., Morigi, M. & Shumyatsky, P. On profinite groups with word values covered by nilpotent subgroups. Isr. J. Math. 226, 993–1008 (2018). https://doi.org/10.1007/s11856-018-1720-2

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  • DOI: https://doi.org/10.1007/s11856-018-1720-2

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