, Volume 139, Issue 1, pp 349-359

The Erdős-Heilbronn problem in Abelian groups

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Abstract

Solving a problem of Erdős and Heilbronn, in 1994 Dias da Silva and Hamidoune proved that ifA is a set ofk residues modulo a primep,p≥2k−3, then the number of different elements of ℤ/pℤ that can be written in the forma+a′ wherea, a′ ∈A,aa′, is at least 2k−3. Here we extend this result to arbitrary Abelian groups in which the order of any nonzero element is at least 2k−3.

Visiting the Rényi Institute of the Hungarian Academy of Sciences. Research partially supported by Hungarian Scientific Research Grants OTKA T043623 and T043631 and the CRM, University of Montreal.