Commutators and projective character tables

There is a necessary and sufficient condition (dating back to Burnside) on the character table of a finite group G for an element to be a commutator, which is g is an element of is a commutator if and only if Sigma(chi epsilon Irr(G)) chi(g)/chi(1) not equal 0 In this paper, consideration will be given to this statement if it is applied to the case of projective characters and show that the corresponding sum becomes a sufficient, but not necessary, condition for g to be an -regulated commutator, where is the underlying 2-cocycle of G.