Olson's constant for the group ℤp⊕ℤp

W. D. Gao, I. Z. Ruzsa, R. Thangadurai

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10 Citations (Scopus)


Let G be a finite abelian group. By Ol(G), we mean the smallest integer t such that every subset A⊂G of cardinality t contains a non-empty subset whose sum is zero. In this article, we shall prove that for all primes p>4.67×1034, we have Ol(ℤp ⊕ ℤp)=p+Ol(ℤp)-1 and hence we have Ol(ℤp⊕ ℤp) ≤p-1+⌈2p+5 log p⌉. This, in particular, proves that a conjecture of Erdos (stated below) is true for the group ℤp⊕ ℤp for all primes p>4.67×1034.

Original languageEnglish
Pages (from-to)49-67
Number of pages19
JournalJournal of Combinatorial Theory. Series A
Issue number1
Publication statusPublished - Jul 1 2004


ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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