Brauer indecomposability of Scott modules

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• 作者：Hiroki Ishioka ; ^{1114701@ed.tus.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Naoko Kunugi ^{kunugi@rs.kagu.tus.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Representations of finite groups ; Fusion systems ; Scott modules
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：470
• 期：Complete
• 页码：441-449
• 全文大小：264 K

文摘

Let k be an algebraically closed field of prime characteristic p, G a finite group and P a p-subgroup of G  . We investigate the relationship between the fusion system class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316303416&_mathId=si1.gif&_user=111111111&_pii=S0021869316303416&_rdoc=1&_issn=00218693&md5=841aab88b1c39386fb5e6b8daa315f0e" title="Click to view the MathML source">F_P(G)class="mathContainer hidden">class="mathCode">${\mathcal{F}}_P(G)$ and the Brauer indecomposability of the Scott kG-module in the case that P is not necessarily abelian. We give an equivalent condition for Scott kG-module with vertex P to be Brauer indecomposable.