Some embeddings between symmetric R. Thompson groups

Julio Aroca*, Collin Bleak

*Corresponding author for this work

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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).
Original languageEnglish
Number of pages18
JournalProceedings of the Edinburgh Mathematical Society
Early online date7 Dec 2021
Publication statusE-pub ahead of print - 7 Dec 2021


  • R Thompson groups
  • Embeddings
  • Topological conjugacy
  • FSS Groups


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