A note on the projective representations of $p$-solvable and $\pi$-separable group

Following Gluck and Wolf we complete the Itô–Michler’s Theorem for the projective representations of a $p$-solvable or $\pi$-separable group, and then we relate the projective irreducible modules of such a group with those of its Sylow $p$-subroups and Hall $\pi$-subgroups.