1 results
Some embeddings between symmetric R. thompson groups
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 1 / February 2022
- Published online by Cambridge University Press:
- 07 December 2021, pp. 1-18
-
- Article
- Export citation
-
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 ${V_n(H)}$
.
