Uniform simplicity of groups with proximal action

Gal, Światosław; Gismatullin, Jakub

doi:10.1090/btran/18

Uniform simplicity of groups with proximal action
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by Światosław R. Gal and Jakub Gismatullin; with an appendix by Nir Lazarovich

Trans. Amer. Math. Soc. Ser. B 4 (2017), 110-130

DOI: https://doi.org/10.1090/btran/18

Published electronically: September 6, 2017

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Abstract:

We prove that groups acting boundedly and order-primitively on linear orders or acting extremely proximally on a Cantor set (the class including various Higman-Thomson groups; Neretin groups of almost automorphisms of regular trees, also called groups of spheromorphisms; the groups of quasi-isometries and almost-isometries of regular trees) are uniformly simple. Explicit bounds are provided.

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