### Abstract

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>4.67×10^{34}, we have Ol(ℤ_{p} ⊕ ℤ_{p})=p+Ol(ℤ_{p})-1 and hence we have Ol(ℤ_{p}⊕ ℤ_{p}) ≤p-1+⌈2p+5 log p⌉. This, in particular, proves that a conjecture of Erdos (stated below) is true for the group ℤ_{p}⊕ ℤ_{p} for all primes p>4.67×10^{34}.

Original language | English |
---|---|

Pages (from-to) | 49-67 |

Number of pages | 19 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 107 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 2004 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

_{p}⊕ℤp.

*Journal of Combinatorial Theory, Series A*,

*107*(1), 49-67. https://doi.org/10.1016/j.jcta.2004.03.007

**Olson's constant for the group ℤ _{p}⊕ℤp.** / Gao, W. D.; Ruzsa, I.; Thangadurai, R.

Research output: Contribution to journal › Article

_{p}⊕ℤp',

*Journal of Combinatorial Theory, Series A*, vol. 107, no. 1, pp. 49-67. https://doi.org/10.1016/j.jcta.2004.03.007

_{p}⊕ℤp. Journal of Combinatorial Theory, Series A. 2004 Jul;107(1):49-67. https://doi.org/10.1016/j.jcta.2004.03.007

}

TY - JOUR

T1 - Olson's constant for the group ℤp⊕ℤp

AU - Gao, W. D.

AU - Ruzsa, I.

AU - Thangadurai, R.

PY - 2004/7

Y1 - 2004/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=3242658435&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3242658435&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2004.03.007

DO - 10.1016/j.jcta.2004.03.007

M3 - Article

AN - SCOPUS:3242658435

VL - 107

SP - 49

EP - 67

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 1

ER -