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  • Hyperlinear groups are motivated by Connes' Embedding Conjecture, which is one of the central unresolved problems in theory of operator algebras, while sofic groups were introduced by Gromov in connection with Gootschalk's Surjunctivity Conjecture (stating that no shift dynamical system AG, where G is a countable group and A is a finite discrete space, contains a proper isomorphic copy of itself).
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