Sofic groups and profinite topology on free groups

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Journal of Algebra, 320(9), 3512–3518 (2008) .


Abstract

We give a definition of weakly sofic groups (w-sofic groups). Our definition is a rather natural extension of the definition of sofic groups where instead of the Hamming metric on symmetric groups we use general bi-invariant metrics on finite groups. The existence of non-w-sofic groups is equivalent to some conjecture about profinite topology on free groups.



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