English

Critical pairs in abelian groups and Kemperman's structure theorem

Number Theory 2007-05-23 v2 Combinatorics

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.

Keywords

Cite

@article{arxiv.math/0508179,
  title  = {Critical pairs in abelian groups and Kemperman's structure theorem},
  author = {Vsevolod F. Lev},
  journal= {arXiv preprint arXiv:math/0508179},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T17:22:57.359Z