Characters of relative p′-degree over normal subgroups

• 成果类型: Article
• 署名作者: Navarro, Gabriel; Pham Huu Tiep
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.178.3.7
• 发表日期: 2013
• 页码: 1135-1171
• 关键词: counting characters; reduction theorem; blocks; question

摘要

Let Z be a normal subgroup of a finite group G, let lambda is an element of Irr(Z) be an irreducible complex character of Z, and let p be a prime number. If p does not divide the integers chi(1)/lambda(1) for all chi is an element of Irr(G) lying over lambda, then we prove that the Sylow p-subgroups of G/Z are abelian. This theorem, which generalizes the Gluck-Wolf Theorem to arbitrary finite groups, is one of the principal obstacles to proving the celebrated Brauer Height Zero Conjecture.