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.
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.
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
\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
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Linking options:
https://www.mathnet.ru/eng/im9101
https://doi.org/10.1070/IM9101
https://www.mathnet.ru/eng/im/v85/i6/p104
This publication is cited in the following 1 articles:
Matteo Cavaleri, Daniele D'Angeli, Alfredo Donno, Emanuele Rodaro, “On a class of poly-context-free groups generated by automata”, Journal of Algebra, 626 (2023), 135
Citation in format AMSBIB
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