Tensor quasi-random groups

Sellke, Mark

doi:10.1090/bproc/86

Tensor quasi-random groups
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Proc. Amer. Math. Soc. Ser. B 9 (2022), 12-21

Abstract:

Gowers [Combin. Probab. Comput. 17 (2008), pp. 363–387] 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.

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