New Proofs of Plünnecke-type Estimates for Product Sets in Groups

Details New Proofs of Plünnecke-type Estimates for Product Sets in Groups New Proofs of Plünnecke-type Estimates for Product Sets in Groups

2011-01-18

arxiv.org/abs/1101.3507v3

Mathematics

Combinatorics

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

Scientific paper

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.

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