The Freiman--Ruzsa Theorem over Finite Fields
Combinatorics
2018-06-07 v3
Abstract
Let G be a finite abelian group of torsion r and let A be a subset of G. The Freiman--Ruzsa theorem asserts that if |A+A| < K|A| then A is contained in a coset of a subgroup of G of size at most r^{K^4}K^2|A|. It was conjectured by Ruzsa that the subgroup size can be reduced to r^{CK}|A| for some absolute constant C >= 2. This conjecture was verified for r = 2 in a sequence of recent works, which have, in fact, yielded a tight bound. In this work, we establish the same conjecture for any prime torsion.
Keywords
Cite
@article{arxiv.1212.5738,
title = {The Freiman--Ruzsa Theorem over Finite Fields},
author = {Chaim Even-Zohar and Shachar Lovett},
journal= {arXiv preprint arXiv:1212.5738},
year = {2018}
}