New necessary conditions on the existence of abelian difference sets

Abstract

In this paper we develop a new method to obtain identities in a group algebraGF(p)G if an abelian difference set of ordern≡0 (modp) exists inG. We give an explicit formula ifp 2 orp 3 is the exactp-power dividingn. This generalizes the approach of Wilbrink, Arasu and the author. The proof presented here uses some knowledge about field extensions of thep-adic numbers.

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Pott, A. New necessary conditions on the existence of abelian difference sets. Combinatorica 12, 89–93 (1992). https://doi.org/10.1007/BF01191207

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AMS subject classification (1991)

  • 05 B 10