A Note on the Gluck-Wolf Theorem

• 来源期刊: 代数集刊（英文版）
• 关键词: p-Brauer character twisted group algebra representation group plength
• 年，卷（期）: 2002,（4）
• 页码范围: 393-397
• 页数: 5页
• 语种: 英文

摘要

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.