Tensor quasi-random groups

Proceedings of the American Mathematical Society, Series B Pub Date : 2021-03-19 DOI:10.1090/bproc/86

Mark Sellke

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引用次数: 1

Abstract

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.

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张量拟随机群

(Combin高尔。Probab。计算，17 (2008)，pp. 363-387]对任意正密度子集a1, a2, a3a_1,A_2,A_3的A 1,A 2,A 3=G的有限群G G进行了优雅的刻画。当且仅当G G不承认常维的非平凡不可约表示时，拟随机性这一性质成立。我们给出了张量拟随机群的对偶刻画，其中子集的乘法用表示的张量积代替。

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来源期刊

Proceedings of the American Mathematical Society, Series B

CiteScore

1.60

自引率

0.00%

发文量