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

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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.

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  1. Department of Mathematics, University of Rochester, Rochester, New York, 14617, USA

    Giorgis Petridis

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  1. Giorgis Petridis
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Correspondence to Giorgis Petridis.

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Petridis, G. New proofs of Plünnecke-type estimates for product sets in groups. Combinatorica 32, 721–733 (2012). https://doi.org/10.1007/s00493-012-2818-5

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  • DOI: https://doi.org/10.1007/s00493-012-2818-5

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