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Israel Journal of Mathematics

, Volume 140, Issue 1, pp 375–380 | Cite as

Additive Latin transversals and group rings

  • W. D. Gao
  • D. J. Wang
Article

Abstract

LetA={a 1, …,a k} and {b 1, …,b k} be two subsets of an abelian groupG, k≤|G|. Snevily conjectured that, when |G| is odd, there is a numbering of the elements ofB such thata i+b i,1≤ik are pairwise distinct. By using a polynomial method, Alon affirmed this conjecture for |G| prime, even whenA is a sequence ofk<|G| elements. With a new application of the polynomial method, Dasgupta, Károlyi, Serra and Szegedy extended Alon’s result to the groupsZ p r andZ p rin the casek<p and verified Snevily’s conjecture for every cyclic group. In this paper, by employing group rings as a tool, we prove that Alon’s result is true for any finite abelianp-group withk<√2p, and verify Snevily’s conjecture for every abelian group of odd order in the casek<√p, wherep is the smallest prime divisor of |G|.

Keywords

Abelian Group Cyclic Group Israel Journal Group Ring Proper Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© The Hebrew University Magnes Press 2004

Authors and Affiliations

  • W. D. Gao
    • 1
  • D. J. Wang
    • 2
  1. 1.Department of Computer Science and TechnologyUniversity of PetroleumBeijingChina
  2. 2.Department of MathematicsTsinghua UniversityBeijingChina

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