Critical pairs in abelian groups and Kemperman's structure theorem

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102165A 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 changesNumber TheoryCombinatoricsMSC-class: 11P70 (Primary) 11B75, 05D99 (Secondary)Critical pairs in abelian groups and Kemperman's structure theoremtext