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Critical pairs in abelian groups and Kemperman's structure theorem

Vsevolod F. Lev
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Abstract

A well-known result by Kemperman describes the structure of those pairs (A,B) of finite subsets of an abelian group satisfying |A+B|\le|A|+|B|-1. We establish a description which is, in a sense, dual to Kemperman's, and as an application sharpen several results due to Deshouillers, Hamidoune, Hennecart, and Plagne.

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Vsevolod F. Lev. 2006-02-03. Critical pairs in abelian groups and Kemperman's structure theorem. https://arxiv.org/abs/math/0508179

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