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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sofic representations of amenable groups


Authors: Gábor Elek and Endre Szabó
Journal: Proc. Amer. Math. Soc. 139 (2011), 4285-4291
MSC (2010): Primary 20F65
Published electronically: July 12, 2011
MathSciNet review: 2823074
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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.


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Additional Information

Gábor Elek
Affiliation: Alfred Renyi Mathematical Institute, Hungarian Academy of Science, P.O. Box 127, Budapest, 1364, Hungary

Endre Szabó
Affiliation: Alfred Renyi Mathematical Institute, Hungarian Academy of Science, P.O. Box 127, Budapest, 1364, Hungary

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11222-X
PII: S 0002-9939(2011)11222-X
Keywords: Sofic groups, amenable groups, amalgamated products.
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.