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We give an alternate proof of a Theorem of Elek and Szabo establishingL\"uck's determinant conjecture for sofic groups. Our proof is based on traceson group C*-algebras. We briefly discuss the relation with Atiyah's problem onthe integrality of $L^2$-Betti numbers.

Traces on group C*-algebras, sofic groups and L\"uck's conjecture