Critical pairs in abelian groups and Kemperman's structure theorem

Details Critical pairs in abelian groups and Kemperman's structure theorem Critical pairs in abelian groups and Kemperman's structure theorem

2005-08-10

arxiv.org/abs/math/0508179v2

Mathematics

Number Theory

20+ pages, (some) typos fixed, other minor changes

Scientific paper

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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