Tensor Quasi-Random Groups

Gowers has elegantly characterized the finite groups $G$ in which $A_1A_2A_3 = G$foranypositivedensitysubsets$A_1,A_2,A_3$. This property, quasi-randomness, holds if and only if G does not admit a nontrivial irreducible representation of constant dimension. We present a dual characterization of tensor quasi-random groups in which multiplication of subsets is replaced by tensor product of representations.