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Some embeddings between symmetric R. Thompson groups

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Embeddings_between_symmetric_Thompson_groups.pdf (316.2Kb)
Date
07/12/2021
Author
Aroca, Julio
Bleak, Collin
Funder
EPSRC
Grant ID
EP/R032866/1
Keywords
R Thompson groups
Embeddings
Topological conjugacy
FSS Groups
QA Mathematics
T-NDAS
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Abstract
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.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/25493

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