Full groups and soficity
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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.References
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Additional Information
- Gábor Elek
- Affiliation: Department of Mathematics, Lancaster University, Bailrigg, Lancaster, LA1 4YW, United Kingdom
- MR Author ID: 360750
- Email: g.elek@lancaster.ac.uk
- 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
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3314104