Sofic representations of amenable groups

Details Sofic representations of amenable groups Sofic representations of amenable groups

2010-10-17

arxiv.org/abs/1010.3424v2

Mathematics

Group Theory

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Scientific paper

Using probabilistic methods, Collins and Dykema proved that the free product of two sofic groups amalgamated over a monotileably 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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