Non self-similar metabelian groups

Q: What type of study is this?

This is a Quantitative Study study.

Dessislava Hristova Kochloukova; Melissa de Sousa Luiz

doi:10.48550/arxiv.2509.05798

September 6, 2025Open Access

Non self-similar metabelian groups

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Key Points

Finitely presented metabelian groups with a Krull dimension of 2 may not be self-similar, indicating a significant structural difference.
The examination reveals specific conditions under which these groups diverge from self-similarity observed in Krull dimension 1.
The research builds on previous work by Kochloukova and Sidki, expanding the understanding of group properties in higher dimensions.
Highlights the unique characteristics of abelian components in the structure of metabelian groups.

Implication

This analysis shows conditions for finitely presented groups not being self-similar in contrast with previous findings.

Abstract

We show some sufficient conditions for a finitely presented group G = A 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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Cite This Study

Kochloukova et al. (2025) studied this question.

synapsesocial.com/papers/68ebffcfdef9fcb308ff2541 https://doi.org/10.48550/arxiv.2509.05798

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Non self-similar metabelian groups

Key Points

Implication

Abstract

Discussion

Cite This Study

Non self-similar metabelian groups

Key Points

Implication

Abstract

Discussion

Cite This Study

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