Projective characters of extra-special p-groups

Abstract

Let G be an extra-special p-group of order for The aim of this paper is to investigate what possible combinations of degrees (counting multiplicities) of irreducible α-characters of G can occur for in the Schur multiplier and then to determine the numbers of that give the same combinations. Solutions are given when n = 2 and in general for Writing G for n > 2 as the central product of two extra-special p-groups E and K, partial solutions are obtained for p odd when (a) every element of E is α-regular for all and (b) and the subgroup of M(G) consisting of with trivial is considered instead.