Full groups and soficity

Elek, Gabor (2015) Full groups and soficity. Proceedings of the American Mathematical Society, 143 (5). pp. 1943-1950. ISSN 0002-9939

Abstract

First, we answer a question of 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.