Let and let be an element in the Higman–Thompson group . We study the structure of the centralizer of through a careful analysis of the action of on the Cantor set . We make use of revealing tree pairs as developed by Brin and Salazar from which we derive discrete train tracks and flow graphs to assist us in our analysis. A consequence of our structure theorem is that element centralizers are finitely generated. Along the way we give a short argument using revealing tree pairs which shows that cyclic groups are undistorted in .
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Collin Bleak, Hannah Bowman, Alison Gordon Lynch, Garrett Graham, Jacob Hughes, Francesco Matucci, Eugenia Sapir, Centralizers in the R. Thompson group . Groups Geom. Dyn. 7 (2013), no. 4, pp. 821–865DOI 10.4171/GGD/207