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Some embeddings between symmetric R. thompson groups

Part of: Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  07 December 2021

Julio Aroca  and
Collin Bleak
Julio Aroca
Affiliation:
Instituto de Ciencias Matemáticas, Madrid, Spain ([email protected])
Collin Bleak
Affiliation:
University of St Andrews, St Andrews, UK ([email protected])
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Abstract

Let $m\leqslant n\in \mathbb {N}$, and $G\leqslant \operatorname {Sym}(m)$ and $H\leqslant \operatorname {Sym}(n)$. In this article, we find conditions enabling embeddings between the symmetric R. Thompson groups ${V_m(G)}$ and ${V_n(H)}$. When $n\equiv 1 \mod (m-1)$, and under some other technical conditions, we find an embedding of ${V_n(H)}$ into ${V_m(G)}$ via topological conjugation. With the same modular condition, we also generalize a purely algebraic construction of Birget from 2019 to find a group $H\leqslant \operatorname {Sym}(n)$ and an embedding of ${V_m(G)}$ into ${V_n(H)}$.

Keywords

R. Thompson groupsembeddingstopological conjugacyFSS Groups

MSC classification

Primary: 20E07: Subgroup theorems; subgroup growth
Secondary: 20E34: General structure theorems 20F65: Geometric group theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 1 , February 2022 , pp. 1 - 18
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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