  Gowers has elegantly characterized the finite groups $G$ in which $A_1A_2A_3
= G$ for any positive density subsets $A_1,A_2,A_3$. 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.
