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The power conjugacy problem in Higman-Thompson groups

Lookup NU author(s): Dr Andrew Duncan, David Robertson



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


An introduction to the universal algebra approach to Higman-Thompson groups (including Thompson's group V) is given, following a series of lectures by Graham Higman in 1973. In these talks, Higman outlined an algorithm for the conjugacy problem; which although essentially correct fails in certain cases, as we show here. A revised and complete version of the algorithm is written out explicitly. From this, we construct an algorithm for the power conjugacy problem in these groups. Python implementations of these algorithms can be found in [26].

Publication metadata

Author(s): Barker N, Duncan AJ, Robertson DM

Publication type: Article

Publication status: Published

Journal: International Journal of Algebra and Computation

Year: 2016

Volume: 26

Issue: 2

Pages: 309-374

Online publication date: 09/03/2016

Acceptance date: 18/01/2016

Date deposited: 26/05/2016

ISSN (print): 0218-1967

ISSN (electronic): 1793-6500

Publisher: World Scientific Publishing Co. Pte. Ltd.


DOI: 10.1142/S0218196716500144


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