Groups, Geometry, and Dynamics

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Volume 10, Issue 2, 2016, pp. 619–648
DOI: 10.4171/GGD/359

Published online: 2016-06-09

Maximal subgroups of multi-edge spinal groups

Theofanis Alexoudas[1], Benjamin Klopsch[2] and Anitha Thillaisundaram[3]

(1) Royal Holloway, University of London, Egham, UK
(2) Heinrich-Heine-Universität, Düsseldorf, Germany
(3) Heinrich-Heine-Universität, Düsseldorf, Germany

A multi-edge spinal group is a subgroup of the automorphism group of a regular $p$-adic rooted tree, generated by one rooted automorphism and a finite number of directed automorphisms sharing a common directing path. We prove that torsion multi-edge spinal groups do not have maximal subgroups of infinite index. This generalizes a result of Pervova for GGS-groups.

Keywords: Multi-edge spinal groups, branch groups, maximal subgroups

Alexoudas Theofanis, Klopsch Benjamin, Thillaisundaram Anitha: Maximal subgroups of multi-edge spinal groups. Groups Geom. Dyn. 10 (2016), 619-648. doi: 10.4171/GGD/359