Tensor Quasi-Random Groups

Mark Sellke

paper

Tensor Quasi-Random Groups

arXiv:2103.11048

Abstract

Gowers has elegantly characterized the finite groups $G$ in which $A_{1} A_{2} A_{3} = G$ 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.