On semilinear sets and asymptotic approximate groups

DOI10.1016/J.AAM.2022.102330OpenAlexW4213445230MaRDI QIDQ2122762

Wolfgang Alexander Moens, Arindam Biswas

Publication date: 7 April 2022

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.05757

zbMATH Keywords

covering numberadditive combinatoricssimplicesapproximate groupsasymptotic approximate groupsgrowth of metric balls in groups

Mathematics Subject Classification ID

Asymptotic properties of groups (20F69) Lattice packing and covering (number-theoretic aspects) (11H31) Additive bases, including sumsets (11B13) Inverse problems of additive number theory, including sumsets (11P70)

Cites Work

• Approximate subgroups of linear groups.
• Nilprogressions and groups with moderate growth
• Every finite subset of an abelian group is an asymptotic approximate group
• The structure of approximate groups.
• Product set estimates for non-commutative groups
• Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).
• Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
• INVERSE THEOREMS FOR SETS AND MEASURES OF POLYNOMIAL GROWTH
• Growth in finite simple groups of Lie type

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