The multiplier conjecture for elementary abelian groups

Applying the method that we presented in [19], in this article we prove: “Let G be an elementary abelian p-group. Let n = dn₁. If d(≠ p) is a prime not dividing n₁, and the order w of d mod p satisfies $ w > frac{{d^2}}{3} $, then the Second Multiplier Theorem holds without the assumption n₁ > λ, except that only one case is yet undecided: w ≤ d², and $ frac{{p - 1}}{{2w}} ge 3 $, and t is a quadratic residue mod p, and t is not congruent to $ x^{frac{{p - 1}}{{2w}}j} $ (mod p) (1 ≤ j < 2w), where t is an integer meeting the conditions of Second Multiplier Theorem, and x is a primitive root of p.”. © 1994 John Wiley & Sons, Inc.