Weakly maximal subgroups in regular branch groups

JOURNAL OF ALGEBRA

卷:455

Article

Bou-Rabee, Khalid¹  Leemann, Paul-Henry²  Nagnibeda, Tatiana² 

[1] CUNY, CCNY, Sch Math, New York, NY 10021 USA

[2] Univ Geneva, Dept Math, Geneva, Switzerland

关键词: Branch groups;    Weakly maximal subgroups;    Grigorchuk group;    Parabolic subgroups;   

DOI  :  10.1016/j.jalgebra.2016.02.009

来源: Elsevier

【 摘 要 】

Let G be a finitely generated regular branch group acting by automorphisms on a regular rooted tree T. It is wellknown 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free