JournalscmhVol. 79 , No. 1DOI 10.1007/s00014-003-0786-5

A new critical pair theorem applied to sum-free sets in Abelian groups

  • Yahya ould Hamidoune

    Université Pierre et Marie Curie, Paris, France
  • Alain Plagne

    Ecole Polytechnique, Palaiseau, France
A new critical pair theorem applied to sum-free sets in Abelian groups cover

Abstract

We shall prove a new generalization of Vosper critical pair theorem to finite Abelian groups. We next apply this new tool to the theory of (k,l)(k,l)-free sets in finite Abelian groups. In particular, in most cases, we describe the structure of maximal (k,l)(k,l)-free sets and determine the maximal cardinality of such a set. This result allows us for instance to give precisions on an old result of Yap: we are able to describe completely the maximal sum-free sets with cardinality at least one third of that of the ambient group.