On the structure of finitely generated subgroups of branch groups

Dominik Francoeur; Rostislav Grigorchuk; Paul-Henry Leemann; Tatiana Nagnibeda

On the structure of finitely generated subgroups of branch groups

Group Theory 2025-04-02 v2

Authors: Dominik Francoeur , Rostislav Grigorchuk , Paul-Henry Leemann , Tatiana Nagnibeda

Abstract

We describe the block structure of finitely generated subgroups of branch groups with the so-called subgroup induction property, including the first Grigorchuk group $\mathcal{G}$ and the torsion GGS groups.

Keywords

branch groups finitely generated subgroups Grigorchuk group GGS groups subgroup induction property block structure

Cite

@article{arxiv.2402.15496,
  title  = {On the structure of finitely generated subgroups of branch groups},
  author = {Dominik Francoeur and Rostislav Grigorchuk and Paul-Henry Leemann and Tatiana Nagnibeda},
  journal= {arXiv preprint arXiv:2402.15496},
  year   = {2025}
}

Comments

35 pages, 3 figures. v2: Final version. The proof of Theorem 6.13 was proving a little bit more than announced, this is now made explicit in remark 6.16

On the structure of finitely generated subgroups of branch groups

Abstract

Keywords

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