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Abstract
Let G be a finitely generated regular branch group acting by automorphisms on a regular rooted tree T. It is well-known that stabilizers of infinite rays in T (aka parabolic subgroups) are weakly maximal subgroups in G, that is, maximal among subgroups of infinite index. We show that, given a finite subgroup Q≤. G, G possesses uncountably many automorphism equivalence classes of weakly maximal subgroups containing Q. In particular, for Grigorchuk-Gupta-Sidki type groups this implies that they have uncountably many automorphism equivalence classes of weakly maximal subgroups that are not parabolic.
Original language | English |
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Pages (from-to) | 347-357 |
Number of pages | 11 |
Journal | Journal of Algebra |
Volume | 455 |
DOIs | |
Publication status | Published - 1 Jun 2016 |
Externally published | Yes |
Keywords
- Branch groups
- Grigorchuk group
- Parabolic subgroups
- Primary
- Secondary
- Weakly maximal subgroups
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Dive into the research topics of 'Weakly maximal subgroups in regular branch groups'. Together they form a unique fingerprint.Activities
- 1 Presentation at conference/workshop/seminar
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Sous-groupes maximaux, faiblement maximaux et généralisations
Paul-Henry Leemann (Speaker)
4 Feb 2025Activity: Talk or presentation › Presentation at conference/workshop/seminar