On the critical pair theory in abelian groups : Beyond Chowla's Theorem
  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. 
Yahya Ould Hamidoune and Oriol Serra and Gilles Zemor