Maximal subgroups of non-torsion Grigorchuk-Gupta-Sidki groups

Abstract

A Grigorchuk-Gupta-Sidki (GGS-)group is a subgroup of the automorphism group of the $p$-adic 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 non-torsion GGS-groups, which include the weakly regular branch, but not branch, GGS-group.

17 pages, minor revisions

References in corpus (3)

• Maximal subgroups of groups of intermediate growth
• On maximal subgroups of infinite index in branch and weakly branch groups
• Pro-$\mathcal{C}$ congruence properties for groups of rooted tree automorphisms

Cited by in corpus (1)

• Subgroup induction property for branch groups