Normal subgroups of non-torsion multi-EGS groups

2025/09/10 by Benjamin Klopsch, Klopsch, Benjamin, Anitha Thillaisundaram +1
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2509.08576

openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the distribution of normal subgroups in non-torsion, regular branch multi-EGS groups and show that the congruence completions of such groups have bounded finite central width. In particular, we show that the profinite completion of the Fabrykowski--Gupta group acting on the p-adic tree has central width 2 for every odd prime p. The methods used also apply to the family of Sunic groups, which closely resemble the Grigorchuk group.

Citations

• On the lower central series of a large family of non-periodic GGS-groups
• The automorphism group of a multi-GGS group
• The derived series of GGS-groups
• Conjugacy classes of polyspinal groups
• The profinite completion of multi-EGS groups
• Maximal subgroups and irreducible representations of generalised\n multi-edge spinal groups
• Maximal subgroups of multi-edge spinal groups
• GGS-groups: order of congruence quotients and Hausdorff dimension
• Hausdorff dimension in a family of self-similar groups
• Profinite completions of some groups acting on trees
• The Fesenko groups have finite width

Related

• The profinite completion of multi-EGS groups
• Maximal subgroups of non-torsion Grigorchuk-Gupta-Sidki groups
• Normal coverings and pairwise generation of finite alternating and symmetric groups
• Multi-EGS-groups: exponent of congruence quotients
• Uniform Diameter Bounds in Branch Groups