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Maximal subgroups of nontorsion Grigorchuk–Gupta–Sidki groups

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  02 November 2021

Dominik Francoeur  and
Anitha Thillaisundaram
Dominik Francoeur
Affiliation:
Instituto de Ciencias Matemáticas, Calle Nicolás Cabrera, no. 13-15, Campus Cantoblanco, Universidad Autónoma de Madrid, 28049 Madrid, Spain e-mail: dominik.francoeur@icmat.es
Anitha Thillaisundaram*
Affiliation:
Centre for Mathematical Sciences, Lund University, 223 62 Lund, Sweden
*
e-mail: anitha.t@cantab.net
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Abstract

A Grigorchuk–Gupta–Sidki (GGS)-group is a subgroup of the automorphism group of the p-regular rooted tree for an odd prime p, generated by one rooted automorphism and one directed automorphism. Pervova proved that all torsion GGS-groups do not have maximal subgroups of infinite index. Here, we extend the result to nontorsion GGS-groups, which include the weakly regular branch, but not branch, GGS-group.

Keywords

GGS-groupsbranch groupsmaximal subgroups

MSC classification

Primary: 20E08: Groups acting on trees
Secondary: 20E28: Maximal subgroups
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 4 , December 2022 , pp. 825 - 844
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Copyright
© Canadian Mathematical Society, 2021

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Footnotes

This research was supported by a London Mathematical Society Research in Pairs (Scheme 4) grant.

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