Critical pairs in abelian groups and Kemperman's structure theorem
Abstract
Description
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.
20+ pages, (some) typos fixed, other minor changes
20+ pages, (some) typos fixed, other minor changes