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Israel Journal of Mathematics

, Volume 139, Issue 1, pp 349–359 | Cite as

The Erdős-Heilbronn problem in Abelian groups

  • Gyula Károlyi
Article

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.

Keywords

Abelian Group London Mathematical Society Congruence Class Small Positive Integer Prime Power Order 
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Copyright information

© Hebrew University 2004

Authors and Affiliations

  1. 1.Department of Algebra and Number TheoryEötvös UniversityBudapestHungary

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