The α-regular classes of the generalized symmetric group

Abstract

The α-regular classes of any finite groupGare important since they are those classes on which the projective characters ofGwith factor set α take non-zero value, and thus a knowledge of the α-regular classes gives the number of irreducible projective representations ofGwith factor set α (see [4]). Here we look at the particular case of the generalized symmetric groupCmwrSl. The analogous problem of constructing the irreducible projective representations ofCmwrSlhas been dealt with in [6] by generalizing Clifford's theory of inducing from normal subgroups, but unfortunately, it is not in general possible to determine the irreducible projective characters (and hence the α-regular classes) by this method.