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Izvestiya: Mathematics, 2021, Volume 85, Issue 6, Pages 1128–1145
DOI: https://doi.org/10.1070/IM9101 (Mi im9101) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

R. I. Grigorchuka, P.-H. Leemannb, T. V. Nagnibedacd

a Mathematical Department, Texas A&M University, USA
b Institut de Mathématiques, Université de Neuchâtel, Neuchâtel, Switzerland
c Section de mathématiques, Université de Genève, Genève, Switzerland
d Saint Petersburg State University
English version PDF (596 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/IM9101
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 $3$-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: just infinite groups, subdirect products, branch groups.
Funding agency Grant number
Agence Nationale de la Recherche ANR-10-LABX-0070
ANR-11-IDEX-0007
Ministry of Science and Higher Education of the Russian Federation 14.W03.31.0030
The authors gratefully acknowledge support of the Swiss National Science Foundation. The second author carried out this work within the framework of the LABEX MILYON (ANR-10-LABX-0070) of the Université de Lyon, within the programme ‘Investissements d’Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). The first and third authors were partly supported by grant no. 14.W03.31.0030 from the Government of the Russian Federation.
Received: 05.09.2020
Bibliographic databases:
Document Type: Article
UDC: 512.544.2
MSC: 20E08, 20E18, 20F07, 20F10, 20F22, 37B05
Language: English
Original paper language: Russian
Citation: R. I. Grigorchuk, P.-H. Leemann, T. V. Nagnibeda, “Finitely generated subgroups of branch groups and subdirect products of just infinite groups”, Izv. Math., 85:6 (2021), 1128–1145
Citation in format AMSBIB
\Bibitem{GriLeeNag21}
\by R.~I.~Grigorchuk, P.-H.~Leemann, T.~V.~Nagnibeda
\paper Finitely generated subgroups of branch groups and subdirect products of just infinite groups
\jour Izv. Math.
\yr 2021
\vol 85
\issue 6
\pages 1128--1145
\mathnet{http://mi.mathnet.ru/eng/im9101}
\crossref{https://doi.org/10.1070/IM9101}
\zmath{https://zbmath.org/?q=an:07480688}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2021IzMat..85.1128G}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85124246525}
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  • https://doi.org/10.1070/IM9101
  • https://www.mathnet.ru/eng/im/v85/i6/p104
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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