Let Formula: see text be a finite Formula: see text-separable group, where Formula: see text is a set of primes. Formula: see text is said to be an Formula: see text-group if every irreducible Formula: see text-partial character of Formula: see text is monomial. We say that Formula: see text is a weak Formula: see text-group if if every monolithic irreducible Formula: see text-partial character of Formula: see text is monomial. We prove in this note that if Formula: see text is a weak Formula: see text-group then Formula: see text is solvable.
Chen et al. (Sat,) studied this question.