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Tensor quasi-random groups

2022
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Proceedings of the American Mathematical Society, Series B
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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.

doi:10.1090/bproc/86
fatcat:fwzxj4lasbekvojjijk5nxmlvy