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 -free sets in finite Abelian groups. In particular, in most cases, we describe the structure of maximal -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.
Cite this article
Yahya ould Hamidoune, Alain Plagne, A new critical pair theorem applied to sum-free sets in Abelian groups. Comment. Math. Helv. 79 (2004), no. 1, pp. 183–207DOI 10.1007/S00014-003-0786-5