On the critical pair theory in abelian groups : Beyond Chowla's Theorem

Yahya Ould Hamidoune (1) , Oriol Serra (2) , Gilles Zemor (3)

1 C&O - Equipe combinatoire et optimisation
2 Research Group on Graph Theory and Combinatorics [Barcelona]
3 IMB - Institut de Mathématiques de Bordeaux

We obtain critical pair theorems for subsets S and T of an abelian group such that |S+T| < |S|+|T|+1. We generalize some results of Chowla, Vosper, Kemperman and a more recent result due to Rodseth and one of the authors.

Domaines: Théorie des nombres [math.NT]

Yahya Ould Hamidoune, Oriol Serra, Gilles Zemor. On the critical pair theory in abelian groups : Beyond Chowla's Theorem. Combinatorica, 2008, 28 (4), pp.441-467. ⟨10.1007/s00493-008-2262-8⟩. ⟨hal-00181453⟩