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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,a∈a′, 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.

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Authors and Affiliations

  1. Department of Algebra and Number Theory, Eötvös University, Pázmány P. sétány 1/C, H-1117, Budapest, Hungary

    Gyula Károlyi

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  1. Gyula Károlyi
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Correspondence to Gyula Károlyi.

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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.

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Károlyi, G. The Erdős-Heilbronn problem in Abelian groups. Isr. J. Math. 139, 349–359 (2004). https://doi.org/10.1007/BF02787556

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  • DOI: https://doi.org/10.1007/BF02787556

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