Brauer characters and normal Sylow p-subgroups

In this paper, we study some variations of the well-known Itô-Michler theorem for p-Brauer characters using various inequalities involving the p-Brauer character degrees of finite groups. Several new criteria for the existence of a normal Sylow p-subgroup of finite groups are obtained using the p-parts and p′-parts of the p-Brauer character degrees.