Some embeddings between symmetric R. Thompson groups

Julio Aroca; Collin Bleak

doi:10.1017/S001309152100047X

Some embeddings between symmetric R. Thompson groups

Julio Aroca^*, Collin Bleak

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 V_m(G) and V_n(H). When n ≡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 generalise a purely algebraic construction of Birget from 2019 to find a group H ≤ Sym(n) and an embedding of V_m(G) into V_n(H).

Original language	English
Number of pages	18
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	FirstView
Early online date	7 Dec 2021
DOIs	https://doi.org/10.1017/S001309152100047X
Publication status	E-pub ahead of print - 7 Dec 2021

Keywords

R Thompson groups
Embeddings
Topological conjugacy
FSS Groups

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10.1017/S001309152100047X

Embeddings between symmetric Thompson groups
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.
Accepted author manuscript, 316 KB

Bi-synchronizing automata: Bi-synchronizing automata, outer automorphism groups of Higman-Thompson groups, and automorphisms of the shift
Bleak, C. P. (PI) & Cameron, P. J. (CoI)
1/05/18 → 30/04/21
Project: Standard

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title = "Some embeddings between symmetric R. Thompson groups",

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).",

keywords = "R Thompson groups, Embeddings, Topological conjugacy, FSS Groups",

author = "Julio Aroca and Collin Bleak",

note = "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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N2 - 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).

AB - 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).

KW - R Thompson groups

KW - Embeddings

KW - Topological conjugacy

KW - FSS Groups

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DO - 10.1017/S001309152100047X

M3 - Article

SN - 0013-0915

VL - FirstView

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

ER -

Some embeddings between symmetric R. Thompson groups

Abstract

Keywords

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Projects

Bi-synchronizing automata: Bi-synchronizing automata, outer automorphism groups of Higman-Thompson groups, and automorphisms of the shift

Cite this