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Bounding the order of a verbal subgroup in a residually finite group

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Abstract

Let w be a group-word. Given a group G, we denote by w(G) the verbal subgroup corresponding to the word w, that is, the subgroup generated by the set Gw of all w-values in G. The word w is called concise in a class of groups X if w(G) is finite whenever Gw is finite for a group G ∈χ. It is a long-standing problem whether every word is concise in the class of residually finite groups. In this paper we examine several families of group-words and show that all words in those families are concise in residually finite groups.

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Acknowledgments

The authors thank the referee for their helpful suggestions. The first and second authors are members of GNSAGA (Indam). The third author was partially supported by FAPDF and CNPq.

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Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione, Università di Padova, Via G. Gradenigo 6/B, 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 Pavel Shumyatsky.

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Detomi, E., Morigi, M. & Shumyatsky, P. Bounding the order of a verbal subgroup in a residually finite group. Isr. J. Math. 253, 771–785 (2023). https://doi.org/10.1007/s11856-022-2378-3

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  • DOI: https://doi.org/10.1007/s11856-022-2378-3

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