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

Access to Document

10.1070/IM9101

Cite this

@article{2d9fc2368c834caaba47e57222148936,

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",

language = "English",

volume = "85",

pages = "1128--1145",

journal = "Izvestiya Mathematics",

issn = "1064-5632",

number = "6",

}

TY - JOUR

T1 - Finitely generated subgroups of branch groups and subdirect products of just infinite groups

AU - Grigorchuk, R. I.

AU - Leemann, P. H.

AU - Nagnibeda, T. V.

PY - 2021/11

Y1 - 2021/11

N2 - 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.

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.

KW - branch groups

KW - just infinite groups

KW - subdirect products

UR - http://www.scopus.com/inward/record.url?scp=85124246525&partnerID=8YFLogxK

U2 - 10.1070/IM9101

DO - 10.1070/IM9101

M3 - Article

AN - SCOPUS:85124246525

SN - 1064-5632

VL - 85

SP - 1128

EP - 1145

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

IS - 6

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Subgroup induction property for branch groups

Sous-groupes maximaux, faiblement maximaux et généralisations

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

Research output

Subgroup induction property for branch groups

Activities

Sous-groupes maximaux, faiblement maximaux et généralisations

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

Cite this