On asymptotic approximate groups in nilpotent groups
Arindam Biswas

TL;DR
This paper investigates the properties of asymptotic approximate groups within virtually nilpotent groups, establishing conditions under which finite sets exhibit approximate group behavior and extending results to certain infinite sets.
Contribution
It demonstrates that finite sets containing large symmetric word balls are asymptotic approximate groups in virtually nilpotent groups and extends to nonabelian semilinear sets.
Findings
Finite sets with large symmetric word balls are asymptotic approximate groups.
Established a nonabelian semilinear-set analogue for infinite sets.
Results apply to virtually nilpotent groups, broadening understanding of approximate groups.
Abstract
Let be a group and let be non-empty. We call an asymptotic -approximate group if, for a fixed dilation factor , the larger product sets can, for all sufficiently large , be covered by a bounded number of left translates of , with the bound independent of . We show that, in virtually nilpotent groups, finite sets whose powers contain a symmetric word ball of radius comparable to are asymptotic approximate groups. We also prove a nonabelian semilinear-set analogue for certain infinite sets in these groups.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
