Structure of finite simple groups and applications of the classification of finite simple groups

有限单群的结构及有限单群分类的应用

• 批准号: 12640030
• 负责人: YAMAKI Hiroyoshi
• 金额: $ 2.5万
• 依托单位: Kumamoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640030/
• 关键词: Finite simple groups; Prime graphs; p-local geometry; 散在型単純群; モンスター単純群

We studied about the structures of finite simple groups and found several properties of finite groups using the classification of finite simple groups.Yamaki proved that either 71 : 35 or L_2(71) is a maximal subgroup of the Monster and studied about odd order maximal subgroups of finite simple groups using prime graphs.Iiyori defined solvable graphs of finite groups with Seichi Abe and studied about the structure of the graphs of finite simple groups. Among other things they proved that the graphs of finite simple groups are connected and not complete. Using these properties of graphs Iiyori generalized P. Hall's theorem on the solvability of finite groups.Sawabe constructed a new p-local geometry which includes several geometries on the sporadic simple groups. He and Uno(0saka University) verified Dade's conjecture for the Lyons-Sims simple groups. Sawabe and Watanabe proved the Alperin's weight conjecture for the principal block with prime inertia index.Chigira studied Bender-Glauberman's book on the solvability of groups of odd order and simplified Suzuki's last paper using Peterfalvi's character theory for the groups of odd order.

研究了有限单群的结构，利用有限单群的分类发现了有限群的几个性质；Yamaki证明了71：35或L 2(71)是Monster的极大子群，并利用素图研究了有限单群的奇数阶极大子群；Iiyori与Seichi Abe定义了有限群的可解图，并研究了有限单群的图的结构.此外，他们还证明了有限单群的图是连通的且不是完全的。利用图的这些性质，Iiyori推广了P.Hall关于有限群可解性的定理。Sawabe构造了一个新的p-局部几何，它包含了零星单群上的几个几何。他和Uno(0saka大学)证实了Dade关于Lyons-Sims简单群的猜想。Sawabe和Watanabe证明了具有素惯性指数的主块的Alperin权猜想。Chigira研究了Bender-Glauberman关于奇数阶群的可解性一书，并利用Petervalvi关于奇数阶群的特征标理论简化了Suzuki的上一篇论文。

项目成果

千吉良直紀, 飯寄信保, 八牧宏美: "Non-abelian Sylow Subgroups of finite groups of even order"Inventiones Mathematical. 139. 525-539 (2000)

Naoki Chiyoshira、Nobuyasu Iyose、Hiromi Yamaki：“偶阶有限群的非交换 Sylow 子群”发明数学 139. 525-539 (2000)

Nobuo Iiyori: "p-Solvability and a generalization of prime graphs of finite groups"To appear in Communication in Algebra.

Nobuo Iiyori：“p-可解性和有限群素图的推广”出现在《代数通讯》中。

澤辺正人, 渡辺アツミ: "On the principal block of finite groups with abelian Sylow p-subgroups"Journal of Algebra. 237. 719-734 (2001)

Masato Sawabe，Atsumi Watanabe：“关于具有交换 Sylow p 子群的有限群的主块”代数杂志 237. 719-734 (2001)。

澤辺正人: "The centric p-radical complex and a related p-local geometry"Mathematical Proceedings of the Cambridge Philosophical Soc. (未定). (2002)

Masato Sawabe：“中心 p 根复形和相关的 p 局域几何”《剑桥哲学学会数学会议录》（TBD）。

流合米奈: "The diameter of the solvable graph of a finite group"Hokkaido Mathematical Journal. 29. 553-561 (2000)

Mena Ryuai：“有限群的可解图的直径”北海道数学杂志 29. 553-561 (2000)。