Sofic groups and profinite topology on free groups

Lev Glebsky, Luis Manuel Rivera

Full text: http://dx.doi.org/10.1016/j.jalgebra.2008.08.008

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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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