On the structure of finitely generated subgroups of branch groups
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.
Authors
- Tatiana Nagnibeda (ORCID: https://orcid.org/0000-0002-7541-9936)
- Dominik Francoeur (ORCID: https://orcid.org/0000-0003-4464-2825)
- Rostislav Grigorchuk (ORCID: https://orcid.org/0000-0002-3067-5477)
- Paul-Henry Leemann (ORCID: https://orcid.org/0000-0003-4173-0731)
Institutions
- University of Geneva (CH)
- Universidad Autónoma de Madrid (ES)
- Xi’an Jiaotong-Liverpool University (CN)
- Texas A&M University (US)
Publication Details
- Journal
- Journal of Combinatorial Algebra
- Published
- 2025-05-14
- DOI
- https://doi.org/10.4171/jca/112
- Citations
- 1
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 5.33