English

Product set phenomena for countable groups

Dynamical Systems 2016-02-22 v2 Group Theory Number Theory

Abstract

We develop in this paper general techniques to analyze local combinatorial structures in product sets of two subsets of a countable group which are "large" with respect to certain classes of (not necessarily invariant) means on the group. As applications of our methods, we extend and quantify a series of recent results by Jin, Bergelson-Furstenberg-Weiss, Beiglb\"ock-Bergelson-Fish, Griesmer and DiNasso-Lupini to general countable groups.

Keywords

Cite

@article{arxiv.1309.4262,
  title  = {Product set phenomena for countable groups},
  author = {MIchael Björklund and Alexander Fish},
  journal= {arXiv preprint arXiv:1309.4262},
  year   = {2016}
}

Comments

51 pages. Minor changes

R2 v1 2026-06-22T01:28:38.789Z