Finitely generated subgroups of branch groups and subdirect products of just infinite groups

R. I. Grigorchuk; P. H. Leemann; T. V. Nagnibeda

doi:10.1070/IM9101

Finitely generated subgroups of branch groups and subdirect products of just infinite groups

R. I. Grigorchuk, P. H. Leemann, T. V. Nagnibeda

Research output: Contribution to journal › Article › peer-review

Abstract

The aim of this paper is to describe the structure of finitely generated subgroups of a family of branch groups containing the first Grigorchuk group and the Gupta-Sidki-group. We then use this to show that all the groups in this family are subgroup separable (LERF). These results are obtained as a corollary of a more general structural statement on subdirect products of just infinite groups.

Original language	English
Pages (from-to)	1128-1145
Number of pages	18
Journal	Izvestiya Mathematics
Volume	85
Issue number	6
DOIs	https://doi.org/10.1070/IM9101
Publication status	Published - Nov 2021
Externally published	Yes

Keywords

branch groups
just infinite groups
subdirect products

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10.1070/IM9101

Cite this

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title = "Finitely generated subgroups of branch groups and subdirect products of just infinite groups",

abstract = "The aim of this paper is to describe the structure of finitely generated subgroups of a family of branch groups containing the first Grigorchuk group and the Gupta-Sidki-group. We then use this to show that all the groups in this family are subgroup separable (LERF). These results are obtained as a corollary of a more general structural statement on subdirect products of just infinite groups.",

keywords = "branch groups, just infinite groups, subdirect products",

author = "Grigorchuk, {R. I.} and Leemann, {P. H.} and Nagnibeda, {T. V.}",

note = "Publisher Copyright: {\textcopyright} 2021 Russian Academy of Sciences (DoM) and London Mathematical Society.",

year = "2021",

month = nov,

doi = "10.1070/IM9101",

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AU - Nagnibeda, T. V.

PY - 2021/11

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AB - The aim of this paper is to describe the structure of finitely generated subgroups of a family of branch groups containing the first Grigorchuk group and the Gupta-Sidki-group. We then use this to show that all the groups in this family are subgroup separable (LERF). These results are obtained as a corollary of a more general structural statement on subdirect products of just infinite groups.

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KW - subdirect products

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Finitely generated subgroups of branch groups and subdirect products of just infinite groups

Abstract

Keywords

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Nouveaux exemples de groupes séparables par les sous-groupes (LERF)

Cite this

Finitely generated subgroups of branch groups and subdirect products of just infinite groups

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Activities

Nouveaux exemples de groupes séparables par les sous-groupes (LERF)

Cite this