Gyula KAROLYI (Budapest) titre: Restricted set addition in Abelian Groups ------ abstract: --------- Let A denote a k-element subset of the cyclic group of order p. Assume that k is at least 5 and the prime p is not smaller than 2k-3. According to the Dias da Silva - Hamidoune theorem, the number of different group elements that has a representation in the form a+b, where a and b denote distict elements of A, is at least 2k-3. We can extend this result to arbitrary Abelian groups in which the order of the smallest nontrivial subgroup is at least 2k-3. Moreover if it is strictly larger than 2k-3, we can prove that the only configurations that attain the lower bound are arithemtic progressions, thus settling a long-standing open problem of Erdos and Heilbronn. The proof depends on a combinatorial version of Hilbert's Nullstellensatz and on the notion of a certain skew product of Abelian groups.