A Correction to the Uniqueness of a Partial Perfect Locality over a Frobenius P-Category

• 来源期刊: 代数集刊（英文版）
• 关键词: group P-category local structure
• 年，卷（期）: 2019,（4）
• 页码范围: 541-559
• 页数: 19页
• 语种: 英文
• DOI: 10.1142/S1005386719000403

摘要

Let p be a prime,P a finite p-group and F a Frobenius P-category.In [Existence,uniqueness and functoriaiity of the perfect locality over a Frobenius P-category,Algebra Colloq.23 (2016) 541-622],we claimed the uniqueness of the partial perfect locality L（x） over any up-closed set （x） of F-selfcentralizing subgroups of P,but recently Bob Oliver exhibits some counter-examples,demanding some revision of our arguments.In this note we show that,up to replacing the perfect localities by the extendable perfect localities over any up-closed set （x） of F-selfcentralizing subgroups of P,our arguments are correct,still proving the existence and the uniqueness of the perfect Fsc-locality,since it is extendable.We take advantage of this revision to simplify some of our arguments.