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