Sofic representations of amenable groups

Elek, Gábor; Szabó, Endre

doi:10.1090/S0002-9939-2011-11222-X

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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