Abstract
Let G be a finite π -solvable group. In this paper, we show that all monomial irreducible Isaacs π -partial character degrees of G are π -number, if and only if G has a normal Hall π ′ -subgroup. Furthermore, let G be a finite π -separable group and let p be prime in π . We prove that if p divides φ ( 1 ) for all non-linear φ ∈ I π ( G ) , then G has a normal p-complement.
Published Version
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