On sofic approximations of non amenable groups

Published 7 Jun 2023 in math.GR, math.DS, math.LO, and math.OA | (2306.04713v2)

Abstract: In this paper we exhibit for every non amenable group that is initially sub-amenable (sometimes also referred to as LEA), two sofic approximations that are not conjugate by any automorphism of the universal sofic group. This addresses a question of Paunescu and generalizes the Elek-Szabo uniqueness theorem for sofic approximations.

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