Groups with prime power Isaacs π-partial character codegrees

Let [Formula: see text] be a set of prime numbers, [Formula: see text] be a prime and [Formula: see text] be a [Formula: see text]-solvable group. We prove in this paper that if [Formula: see text] is [Formula: see text]-power for every nonlinear, monomial and monolithic [Formula: see text], then [Formula: see text] has a normal Hall [Formula: see text]-subgroup.