Weak Mπ′-groups

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.