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Transactions of the American Mathematical Society Series B

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Uniform simplicity of groups with proximal action


Authors: Światosław R. Gal and Jakub Gismatullin; with an appendix by Nir Lazarovich
Journal: Trans. Amer. Math. Soc. Ser. B 4 (2017), 110-130
MSC (2010): Primary 20E08, 20E32; Secondary 20F65, 22E40
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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Światosław R. Gal
Affiliation: Instytut Matematyczny, Uniwersytetu Wrocławskiego, pl. Grunwaldzki \nicefrac24, 50-384 Wrocław, Poland – and – Weizmann Institute of Science, Rehovot 76100, Israel
Email: sgal@math.uni.wroc.pl

Jakub Gismatullin
Affiliation: Instytut Matematyczny, Uniwersytetu Wrocławskiego, pl. Grunwaldzki \nicefrac24, 50-384 Wrocław, Poland – and – Instytut Matematyczny, Polskiej Akademii Nauk, ul. Śniadeckich 8, 00-656 Warszawa, Poland
Email: gismat@math.uni.wroc.pl

Nir Lazarovich
Affiliation: Departement Mathematik, Eidgenössische Technische Hochschule Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
Email: nir.lazarovich@math.ethz.ch

DOI: https://doi.org/10.1090/btran/18
Keywords: Boundedly simple groups, trees, automorphism groups, spheromorphisms, almost automorphisms, Higman-Thomson groups, Neretin group
Received by editor(s): June 14, 2016
Received by editor(s) in revised form: February 27, 2017
Published electronically: September 6, 2017
Additional Notes: The research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 291111. The first author partially supported by Polish National Science Center (NCN) grant 2012/06/A/ST1/00259 and the European Research Council grant No. 306706.
The second author is partially supported by the NCN grants 2014/13/D/ST1/03491, 2012/07/B/ST1/03513.
Article copyright: © Copyright 2017 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)

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