Some embeddings between symmetric R. Thompson groups
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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).
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
Proceedings of the Edinburgh Mathematical Society
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.
DescriptionFunding: 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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