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The profinite completion of accessible groups

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Abstract

We introduce a class \({\mathcal {A}}\) of finitely generated residually finite accessible groups with a certain natural restriction on one-ended vertex groups in their JSJ-decompositions. We prove that the profinite completion of groups in \({\mathcal {A}}\) almost detects its JSJ-decomposition and compute the genus of free products of groups in \({\mathcal {A}}\).

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Funding

CNPq, Grant number (304146/2020-0).

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Author notes

  1. Dedicated to Wolfgang Herfort on the occasion of his 75-th birthday.

Authors and Affiliations

  1. Federal University of Viçosa: Universidade Federal de Viçosa, Viçosa, Brazil

    Vagner R. de Bessa

  2. Federal University of the Jequitinhonha and Mucuri Valleys, Teófilo Otoni, Brazil

    Anderson L. P. Porto

  3. University of Brasilia: Universidade de Brasilia, Brasilia, Brazil

    Pavel A. Zalesskii

Authors
  1. Vagner R. de Bessa
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  2. Anderson L. P. Porto
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  3. Pavel A. Zalesskii
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Corresponding author

Correspondence to Pavel A. Zalesskii.

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Communicated by John S. Wilson.

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de Bessa, V.R., Porto, A.L.P. & Zalesskii, P.A. The profinite completion of accessible groups. Monatsh Math 202, 217–227 (2023). https://doi.org/10.1007/s00605-022-01789-9

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  • DOI: https://doi.org/10.1007/s00605-022-01789-9

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