The Inductive Blockwise Alperin Weight Condition for PSP4(q)

• 来源期刊: 代数集刊（英文版）
• 关键词: blockwise Alperin weight conjecture inductive blockwise Alperin weight condition PSP4(q)
• 年，卷（期）: 2019,（3）
• 页码范围: 361-386
• 页数: 26页
• 语种: 英文
• DOI: 10.1142/S1005386719000270

摘要

Let G be a finite group and e be any prime dividing ｜G｜.The blockwise Alperin weight conjecture states that the number of the irreducible Brauer characters in an e-block B of G equals the number of the G-conjugacy classes of e-weights belonging to B.Recently,this conjecture has been reduced to the simple groups,which means that to prove the blockwise Alperin weight conjecture,it suffices to prove that all non-abelian simple groups satisfy the inductive blockwise Alperin weight condition.In this paper,we verify this inductive condition for the finite simple groups PSP4(q) and non-defining characteristic,where q is a power of an odd prime.