We show that the free E∞-algebra on a zero-cell cannot be modeled by a commutative Γ-ring. The proof shows that Dyer-Lashof operations of positive degree must vanish on the zero'th homology of such an object.
"Commutative Γ-rings do not model all commutative ring spectra." Homology Homotopy Appl. 11 (2) 189 - 194, 2009.