Maximal subgroups and irreducible representations of generalised multi-edge spinal groups

Thillaisundaram, Anitha and Klopsch, Benjamin (2018) Maximal subgroups and irreducible representations of generalised multi-edge spinal groups. Proceedings of the Edinburgh Mathematical Society, 61 (3). pp. 673-703. ISSN 0013-0915

Full content URL: https://doi.org/10.1017/S0013091517000451

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Abstract

Let p≥3 be a prime. A generalised multi-edge spinal group is a subgroup of the automorphism group of a regular p-adic rooted tree T that is generated by one rooted automorphism and p families of directed automorphisms, each family sharing a common directed path disjoint from the paths of the other families.
This notion generalises the concepts of multi-edge spinal groups, including the widely studied GGS-groups, and the extended Gupta-Sidki groups that were introduced by Pervova. Extending techniques that were developed in these more special cases, we prove: generalised multi-edge spinal groups that are torsion have no maximal subgroups of infinite index. Furthermore we use tree enveloping algebras, which were introduced by Sidki and Bartholdi, to show that certain generalised multi-edge spinal groups admit faithful infinite dimensional irreducible representations over the prime field Z/pZ.

Keywords:tree automorphism, branch groups, maximal subgroups, irreducible representations
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:28317
Deposited On:16 Aug 2017 15:34

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