Skip to main content
Open Access Publications from the University of California

UC San Diego

UC San Diego Previously Published Works bannerUC San Diego

The Freiman-Ruzsa theorem over finite fields

Published Web Location
No data is associated with this publication.

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 K2rK4|A|. It was conjectured by Ruzsa that the subgroup size can be reduced to r C K|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. © 2014 Elsevier Inc.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Item not freely available? Link broken?
Report a problem accessing this item