Skip to main content
SpringerLink
Log in

The conjugacy problem for symmetric Thompson-like groups

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper we generalize techniques of Belk-Matucci [2] to solve the conjugacy problem for every symmetric Thompson-like group Vn(H), where n ≥ 2 and H is a subgroup of the symmetric group on n elements. We use this to prove that, if n ≠ m, Vn(H) is not isomorphic to Vm(G) for any H, G.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Aramayona and L. Funar, Asymptotic mapping class groups of closed surfaces punctured along cantor sets, Moscow Mathematical Journal 21 (2021), 1–29.

    Article  MathSciNet  Google Scholar 

  2. J. Belk and F. Matucci, Conjugacy and dynamics in Thompson’s groups, Geometriae Dedicata 169 (2014), 239–261.

    Article  MathSciNet  Google Scholar 

  3. C. Bleak, C. Donoven and J. Jonušas, Some isomorphism results for Thompson-like groups Vn(G), Israel Journal of Mathematics 222 (2017), 1–19.

    Article  MathSciNet  Google Scholar 

  4. J. W. Cannon, W. J. Floyd and W. R. Parry, Introductory notes on Richard Thompson’s groups, Enseignement Mathématique 42 (1996), 215–256.

    MathSciNet  MATH  Google Scholar 

  5. D. S. Farley and B. Hughes, Finiteness properties of some groups of local similarities, Proceedings of the Edinburgh Mathematical Society 58 (2015), 379–402.

    Article  MathSciNet  Google Scholar 

  6. L. Funar and Y. Neretin, Diffeomorphism groups of tame Cantor sets and Thompson-like groups, Compositio Mathematica 154 (2018), 1066–1110.

    Article  MathSciNet  Google Scholar 

  7. G. Higman, Finitely Presented Infinite Simple Groups, Notes on Pure Mathematics, Vol. 8, Department of Pure Mathematics, Department of Mathematics, I.A.S. Australian National University, Canberra, 1974.

    Google Scholar 

  8. V. V. Nekrashevych, Cuntz-Pimsner algebras of group actions, Journal of Operator Theory 52 (2004), 223–249.

    MathSciNet  MATH  Google Scholar 

  9. M. H. A. Newman, On theories with a combinatorial definition of “equivalence”, Annals of Mathematics 43 (1942), 223–243.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author would like to thank his advisor Javier Aramayona for conversations and support, James Belk for conversations that culminated in what is Section 4 of the present version, and Motoko Kato, Diego López, Waltraud Lederle and Gil Goffer for comments. He is also grateful to the reviewer for suggestions and comments. Finally, he acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554) and the grant MTM2015-67781.

Author information

Authors and Affiliations

  1. Instituto de Ciencias Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, C/ Nicoláqs Cabrera, 13-15, E-28049, Madrid, Spain

    Julio Aroca

Authors
  1. Julio Aroca
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Julio Aroca.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aroca, J. The conjugacy problem for symmetric Thompson-like groups. Isr. J. Math. 244, 49–73 (2021). https://doi.org/10.1007/s11856-021-2169-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-021-2169-2

Search

Navigation