Gowers [Combin. Probab. Comput. 17 (2008), pp. 363–387] elegantly characterized the finite groups
G
G
in which
A
1
A
2
A
3
=
G
A_1A_2A_3=G
for any positive density subsets
A
1
,
A
2
,
A
3
A_1,A_2,A_3
. This property, quasi-randomness, holds if and only if
G
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.