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

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 $(k,l)$-free sets in finite Abelian groups. In particular, in most cases, we describe the structure of maximal $(k,l)$-free sets and determine the maximal cardin...

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Bibliographic Details
Published in:Commentarii mathematici Helvetici 2004-01, Vol.79 (1), p.183-207
Main Authors: Hamidoune, Yahya ould, Plagne, Alain
Format: Article
Language:English
Subjects:
Group theory and generalizations
Number theory
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Summary: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 $(k,l)$-free sets in finite Abelian groups. In particular, in most cases, we describe the structure of maximal $(k,l)$-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.
ISSN:0010-2571
1420-8946
DOI:10.1007/s00014-003-0786-5