Submission date: 31 January 2013.

Abstract:

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman-Ruzsa theorem.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1301.7718 : pdf, ps.