Some embeddings between symmetric R. Thompson groups

Let m ≤ n ∈ ℕ, and G ≤ Sym(m) and H ≤ Sym(n). In this article we find conditions enabling embeddings between the symmetric R. Thompson groups Vm(G) and Vn(H). When n ≡1 mod (m −1), and under some other technical conditions, we find an embedding of Vn(H) into Vm(G) via topological conjugation. With the same modular condition we also generalise a purely algebraic construction of Birget from 2019 to find a group H ≤ Sym(n) and an embedding of Vm(G) into Vn(H).

Citation

Aroca , J & Bleak , C 2021 , ' Some embeddings between symmetric R. Thompson groups ' , Proceedings of the Edinburgh Mathematical Society , vol. FirstView . https://doi.org/10.1017/S001309152100047X

Publication

Proceedings of the Edinburgh Mathematical Society

Status

Peer reviewed

DOI

https://doi.org/10.1017/S001309152100047X

ISSN

0013-0915

Type

Journal article

Rights

Copyright © 2021 the Author(s). Published by Cambridge University Press on behalf of The Edinburgh Mathematical Society. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/S001309152100047X.

Description

Funding: The first author wants to acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Program for Centres of Excellence in R&D” (SEV-2015-0554). The second author wishes to acknowledge support from EPSRC grant EP/R032866/1 during the creation of this paper.

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/25493