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On the structure of finitely generated subgroups of branch groups

  • Dominik Francoeur

    Universidad Autónoma de Madrid, Madrid, Spain
    ORCID

  • Rostislav Grigorchuk

    Texas A&M University, College Station, USA
    ORCID

  • Paul-Henry Leemann

    Xi’an Jiaotong-Liverpool University, Suzhou, P. R. China

  • Tatiana Nagnibeda

    Université de Genève, Geneva, Switzerland
    ORCID
On the structure of finitely generated subgroups of branch groups cover
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Abstract

Motivated by the study of profinite topology in branch groups, we prove a structural result about their finitely generated subgroups. More precisely, we show that finitely generated subgroups of a branch group with the subgroup induction property have a block structure, which roughly means that, up to a finite index, they are products of finite index subgroups, embedded in the group in a way that is coherent with its branch action on the rooted tree.

Cite this article

Dominik Francoeur, Rostislav Grigorchuk, Paul-Henry Leemann, Tatiana Nagnibeda, On the structure of finitely generated subgroups of branch groups. J. Comb. Algebra (2025), published online first

DOI 10.4171/JCA/112