Skip to content

Research at St Andrews

Some isomorphism results for Thompson-like groups Vn(G) 

Research output: Research - peer-reviewArticle



Collin Bleak, Casey Donoven, Julius Jonusas

School/Research organisations


We find some perhaps surprising isomorphism results for the groups {Vn(G)}, where Vn(G) is a supergroup of the Higman–Thompson group Vn for n ∈ N and G ≤ Sn, the symmetric group on n points. These groups, introduced by Farley and Hughes, are the groups generated by Vn and the tree automorphisms [α]g defined as follows. For each g ∈ G and each node α in the infinite rooted n-ary tree, the automorphisms [α]g acts iteratively as g on the child leaves of α and every descendent of α. In particular, we show that Vn ≅ Vn(G) if and only if G is semiregular (acts freely on n points), as well as some additional sufficient conditions for isomorphisms between other members of this family of groups. Essential tools in the above work are a study of the dynamics of the action of elements of Vn(G) on the Cantor space, Rubin’s Theorem, and transducers from Grigorchuk, Nekrashevych, and Suschanskiĭ’s rational group on the n-ary alphabet.


Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 8 Nov 2017

    Research areas

  • Presented simple-groupsS, Finiteness properties, Local similarities, Automata groups

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Some undecidability results for asynchronous transducers and the Brin-Thompson group 2V

    Belk, J. & Bleak, C. May 2017 In : Transactions of the American Mathematical Society. 369, 5, p. 3157-3172 16 p.

    Research output: Research - peer-reviewArticle

  2. The infinite simple group V of Richard J. Thompson: presentations by permutations

    Bleak, C. & Quick, M. 2017 In : Groups, Geometry, and Dynamics. 11, 4, p. 1401-1436 36 p.

    Research output: Research - peer-reviewArticle

  3. Embeddings into Thompson's group V and coCF groups

    Bleak, C., Matucci, F. & Neunhöffer, M. Oct 2016 In : Journal of the London Mathematical Society. 94, 2, p. 583-597 15 p.

    Research output: Research - peer-reviewArticle

  4. The further chameleon groups of Richard Thompson and Graham Higman: Automorphisms via dynamics for the Higman groups G_{n,r}

    Bleak, C., Cameron, P., Maissel, Y., Navas, A. & Olukoya, F. 30 May 2016 (Submitted) In : Mathematics arXiv. 44 p.

    Research output: ResearchArticle

  5. Ideal structure of the C*-algebra of Thompson group T

    Bleak, C. & Juschenko, K. 25 Apr 2016 (Accepted/In press) Topological Methods in Geometric Group Theory. Cambridge University Press, 10 p. (London Mathematical Society Lecture Note Series)

    Research output: Research - peer-reviewChapter (peer-reviewed)

Related by journal

  1. Equilibrium states, pressure and escape for multimodal maps with holes

    Demers, M. F. & Todd, M. Sep 2017 In : Israel Journal of Mathematics. 221, 1, p. 367-424 58 p.

    Research output: Research - peer-reviewArticle

  2. Distance sets, orthogonal projections, and passing to weak tangents

    Fraser, J. M. 25 Jul 2017 (Accepted/In press) In : Israel Journal of Mathematics.

    Research output: Research - peer-reviewArticle

  3. Chains of subsemigroups

    Cameron, P. J., Gadouleau, M., Mitchell, J. D. & Peresse, Y. Jun 2017 In : Israel Journal of Mathematics. 220, 1, p. 479-508

    Research output: Research - peer-reviewArticle

  4. Inflations of geometric grid classes of permutations

    Albert, M. D., Ruskuc, N. & Vatter, V. Feb 2015 In : Israel Journal of Mathematics. 205, 1, p. 73-108 36 p.

    Research output: Research - peer-reviewArticle

ID: 231626997