Subsets of virtually nilpotent groups with the SBM property

DOI10.1007/s10801-023-01250-6zbMath1526.20052arXiv2206.10683OpenAlexW4381737088MaRDI QIDQ6083974

Ryan Burkhart, Isaac Goldbring

Publication date: 31 October 2023

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.10683

zbMATH Keywords

combinatoricsnilpotent groupnonstandard analysisnumber theorycombinatorial number theory

Mathematics Subject Classification ID

Generalizations of solvable and nilpotent groups (20F19) Nilpotent groups (20F18) Density, gaps, topology (11B05) Ramsey theory (05D10) Nonstandard models in mathematics (03H05) Ordered groups (group-theoretic aspects) (20F60)

Cites Work

• Gromov's theorem on groups of polynomial growth and elementary logic
• Some nonstandard methods in combinatorial number theory
• Sumsets contained in infinite sets of integers
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• A proof of a sumset conjecture of Erdős
• Asymptotic cones of finitely presented groups
• Nonstandard methods in Ramsey theory and combinatorial number theory
• Growth of finitely generated solvable groups and curvature of Riemannian manifolds
• The sumset phenomenon
• Separable and tree-like asymptotic cones of groups
• Stable group theory and approximate subgroups
• On Supra-SIM Sets of Natural Numbers
• On Infinite-Difference Sets
• On the Asymptotics of the Growth of 2-Step Nilpotent Groups
• Croissance des boules et des géodésiques fermées dans les nilvariétés
• Ultrafilters Throughout Mathematics
• On the rate of convergence to the asymptotic cone for nilpotent groups and subFinsler geometry
• On groups with locally compact asymptotic cones
• The Theory of Nilpotent Groups
• The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups