Complete settling of the multiplier conjecture for the case of n =3pr

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In this paper we improve the character approach to the multiplier conjecture that we presented after 1992, and thus we have made considerable progress in the case of n=3n1. We prove that in the case of n = 3n1 Second multiplier theorem remains true if the assumption "n1 >λ" is replaced by "(n1, λ)=1".Consequentially we prove that if we let D be a (v, κ,λ)-difference set in an abelian group G, and n=3pr for some prime p, (p,v)=1, then p is a numerical multiplier of D.
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