,A Note on the Gluck-Wolf Theorem

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Let N be a normal subgroup of a finite group G. Let (ψ) be an irreducible Brauer character of N. Assume π is a set of primes and x(1)/(ψ)(1) is a π’-number for any X ∈ Ibrp(G|(ψ)). We prove that, ifp (/|)|G: N|, then G/N has an abelian Hall-π subgroup. If p (∈/)π, then G/N has a metabelian Hall-π subgroup.
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