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


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|.


Abelian Group Cyclic Group Israel Journal Group Ring Proper Subgroup 
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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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