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arXiv · 2509.05798

Non self-similar metabelian groups

Dessislava Hristova Kochloukova·Melissa de Sousa Luiz
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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.

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Dessislava Hristova Kochloukova, Melissa de Sousa Luiz. 2025-09-06. Non self-similar metabelian groups. https://arxiv.org/abs/2509.05798

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