Relative M-groups and relative Mp-groups

Let [Formula: see text] be a finite group and [Formula: see text] be a prime. Denote by [Formula: see text] the set of irreducible [Formula: see text]-)Brauer characters of [Formula: see text]. Let [Formula: see text] be a normal subgroup of [Formula: see text]. [Formula: see text] is said to be a relative [Formula: see text]-group with respect to [Formula: see text] if for every Brauer character [Formula: see text], there exists a subgroup [Formula: see text] of [Formula: see text] containing [Formula: see text] and [Formula: see text] such that [Formula: see text] and [Formula: see text]. We obtain some results about relative [Formula: see text]-groups in this note.