Approximations of groups, characterizations of sofic groups, and equations over groups

We give new characterizations of sofic groups: – A group G is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups.– A group G is sofic if and only if any system of equations solvable in all alternating groups is solvable over G.The last characterization allows to express soficity of an existentially closed group by ∀∃-sentences. © 2016 Elsevier Inc.

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