Non self-similar metabelian groups

2025/09/06 by Dessislava Hristova Kochloukova, Kochloukova, Dessislava Hristova, Melissa de Sousa Luiz +1
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2509.05798

openalex publication_date 2025/09/06 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We show some sufficient conditions for a finitely presented group G = A \rtimes Q, with A and Q abelian and the Krull dimension of A equals to 2 to be not self-similar. This is in contrast to the case of the Krull dimension of A equals to 1 considered by Kochloukova and Sidki in 2020.

Citations

• Which Nilpotent Groups are Self-Similar?
• Intransitive Self-similar Groups
• Lamplighter groups, bireversible automata and rational series over\n finite rings
• On self-similarity of wreath products of abelian groups
• An addendum to `A rigidity property for the set of all characters induced by valuations'

Related

• Self-similarity of some soluble relatively free groups
• Self-similar products of groups
• Self-similar groups of type FP_n
• A new look at finitely generated metabelian groups
• Self-similar groups and topological dimension