New-type Quasirandom Groups and Applications Article Swipe

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YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2308.01504

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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Product (mathematics) Group (periodic table) Type (biology) Mathematics Set (abstract data type) Tuple Plane (geometry) Combinatorics Field (mathematics) Direct product Pure mathematics Discrete mathematics Physics Computer science Geometry Quantum mechanics Biology Programming language Ecology

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2308.01504
PDF: https://arxiv.org/pdf/2308.01504
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4385967613

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DOI: https://doi.org/10.48550/arxiv.2308.01504

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Title: New-type Quasirandom Groups and Applications

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-08-03

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Authors: Thang Pham, Boqing Xue

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Landing page: https://arxiv.org/abs/2308.01504

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Concepts: Product (mathematics), Group (periodic table), Type (biology), Mathematics, Set (abstract data type), Tuple, Plane (geometry), Combinatorics, Field (mathematics), Direct product, Pure mathematics, Discrete mathematics, Physics, Computer science, Geometry, Quantum mechanics, Biology, Programming language, Ecology

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