Sofic representations of amenable groups
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- by Gábor Elek and Endre Szabó
- Proc. Amer. Math. Soc. 139 (2011), 4285-4291
- DOI: https://doi.org/10.1090/S0002-9939-2011-11222-X
- Published electronically: July 12, 2011
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Abstract:
Using probabilistic methods, Collins and Dykema proved that the free product of two sofic groups amalgamated over a monotileabe amenable subgroup is sofic as well. We show that the restriction is unnecessary; the free product of two sofic groups amalgamated over an arbitrary amenable subgroup is sofic. We also prove a group-theoretical analogue of a result of Kenley Jung. A finitely generated group is amenable if and only if it has only one sofic representation up to conjugacy equivalence.References
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Bibliographic Information
- Gábor Elek
- Affiliation: Alfred Renyi Mathematical Institute, Hungarian Academy of Science, P.O. Box 127, Budapest, 1364, Hungary
- MR Author ID: 360750
- Endre Szabó
- Affiliation: Alfred Renyi Mathematical Institute, Hungarian Academy of Science, P.O. Box 127, Budapest, 1364, Hungary
- Received by editor(s): October 25, 2010
- Published electronically: July 12, 2011
- Additional Notes: Research sponsored by OTKA Grants No. 69062 and NK 78439
- Communicated by: Jonathan I. Hall
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 4285-4291
- MSC (2010): Primary 20F65
- DOI: https://doi.org/10.1090/S0002-9939-2011-11222-X
- MathSciNet review: 2823074