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Full groups and soficity


Author: Gábor Elek
Journal: Proc. Amer. Math. Soc. 143 (2015), 1943-1950
MSC (2010): Primary 20F65, 37A20
DOI: https://doi.org/10.1090/S0002-9939-2014-12403-8
Published electronically: December 9, 2014
MathSciNet review: 3314104
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Abstract: First, we answer a question of Giordano and Pestov by proving that the full group of a sofic equivalence relation is a sofic group. Then, we give a short proof of the theorem of Grigorchuk and Medynets that the topological full group of a minimal Cantor homeomorphism is LEF. Finally, we show that for certain non-amenable groups all the generalized lamplighter groups are sofic.


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Additional Information

Gábor Elek
Affiliation: Department of Mathematics, Lancaster University, Bailrigg, Lancaster, LA1 4YW, United Kingdom
Email: g.elek@lancaster.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2014-12403-8
Received by editor(s): November 18, 2012
Received by editor(s) in revised form: November 6, 2013
Published electronically: December 9, 2014
Additional Notes: This work was supported in part by a Marie Curie grant, TAMOP 4.2.1/B-09/1/KMR-2010-003 and MTA Renyi “Lendulet” Groups and Graphs Research Group
Communicated by: Varghese Mathai
Article copyright: © Copyright 2014 American Mathematical Society

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