English

New Proofs of Pl\"unnecke-type Estimates for Product Sets in Groups

Combinatorics 2013-09-10 v3 Number Theory

Abstract

We present a new method to bound the cardinality of triple product sets in groups and give three applications. A new and unexpectedly short proof of the Plunnecke-Ruzsa sumset inequalities for Abelian groups. A new proof of a theorem of Tao on triple products, which generalises these inequalities when no assumption on commutativity is made. A further generalisation of the Plunnecke-Ruzsa inequalities in general groups.

Keywords

Cite

@article{arxiv.1101.3507,
  title  = {New Proofs of Pl\"unnecke-type Estimates for Product Sets in Groups},
  author = {Giorgis Petridis},
  journal= {arXiv preprint arXiv:1101.3507},
  year   = {2013}
}

Comments

15 pages Same results as before. Changes in the introduction and presentation