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arXiv · 2308.01504

New-type Quasirandom Groups and Applications

Thang Pham·Boqing Xue
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Abstract

This paper aims to introduce a more general definition of quasirandom groups and generalize several well-known results in the literature in this new setting. More precisely, let $G$ be a semi-direct product of groups and $X\subseteq G$, we provide conditions such that one can find tuples $(x_0, \ldots, x_k)\in X^{k+1}$ satisfying $x_1x_2\ldots x_k=x_0$ or conditions to guarantee that the product set $XX$ grows exponentially. In a special case of the group of rigid-motions in the plane over an arbitrary finite field, our results offer a reasonably complete description of structures of this group.

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Thang Pham, Boqing Xue. 2023-08-25. New-type Quasirandom Groups and Applications. https://arxiv.org/abs/2308.01504

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