New-type Quasirandom Groups and Applications

2023/08/03 by Thang Pham, Boqing Xue, Pham, Thang +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2308.01504

openalex publication_date 2023/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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⊆ G, we provide conditions such that one can find tuples (x₀, …, x_k)∈ X^k+1 satisfying x₁x₂… x_k=x₀ 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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