Combinatorica

, Volume 32, Issue 6, pp 721–733 | Cite as

New proofs of Plünnecke-type estimates for product sets in groups

Original paper

Abstract

We present a new method to bound the cardinality of product sets in groups and give three applications. A new and unexpectedly short proof of the Plünnecke-Ruzsa sumset inequalities for commutative 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 Plünnecke-Ruzsa inequalities in general groups.

Mathematics Subject Classification (2000)

11P70 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA

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