Applications of the classification of finite simple groups and prime graphs

有限单群和素图分类的应用

• 批准号: 14540034
• 负责人: YAMAKI Hiroyoshi
• 金额: $ 2.3万
• 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: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540034/
• 关键词: Finite simple groups; Prime graphs; p-local geometry; ビルディング

We studied about the structures of finite simple groups and found several properties of finite groups using the classification of finite simple groups.Using properties of solvable graphs of finite groups 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 proved that the reduced Lefschetz module of the G-poset consisting of all centric p-radical subgroups of a finite group G is an χ-projective virtual Zp[G]-module where χ is a family of p-subgroups of the normalizers of the non-centric p-radical subgroups of G.Chigira studied Bender-Glauberman's idea on the proof of Burnside's conjecture and simplified Suzuki's last paper using Peterfalvi's character theory for the groups of odd order. Chigira also gave an elementary construction of Mathieu simple groups M_<11> and M_<12>.Endo gave a generalization of the Maillet determinant and the Demyanenko matrix.

研究了有限单群的结构，利用有限单群的分类得到了有限群的几个性质，利用有限群的可解图的性质，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，它包含了散在单群上的几个几何.他证明了由有限群G的所有中心p-根式子群组成的G-偏序集的约化Lefschetz模是χ-投射虚Zp[G]-模，其中χ是G的非中心p-根式子群的正规化子的p-子群族。Glauberman的想法的证明伯恩赛德的猜想和简化铃木的最后文件使用Peterfalvi的字符理论的群体的奇数秩序。Chigira给出了Mathieu单群M_和M_的初等构造<11><12>，Endo给出了Maillet行列式和Demyanenko矩阵的推广.

项目成果

Masato Sawabe: "The centric p-radical complex and a related p-local geometry"Mathematical Proceedings of the Cambridge Philosophical Society. 133. 383-398 (2002)

Masato Sawabe：“中心 p 根复形和相关的 p 局域几何”剑桥哲学会数学会刊。

流合未奈: "The prime graph of a sporadic simple group"To appear in Communications in Algebra. (印刷中). (2003)

Mina Ryuai：“零星简单群的素图”出现在《代数通讯》（2003 年出版）中。

澤辺正人, 宇野勝博: "Conjectures on character degrees for the simple Lyons group"Quartely Journal of Mathematics. 54. 103-121 (2003)

Masato Sawabe，Katsuhiro Uno：“简单里昂群的特征度猜想”数学季刊 54. 103-121 (2003)。

飯寄 信保: "p-Solvability and a generalization of prime graphs of finite groups"Communications in Algebra. 30. 1679-1691 (2002)

Nobuyasu Iyori：“p-可解性和有限群素图的推广”通讯代数 30. 1679-1691 (2002)

澤辺正人: "The centric p-radical complex and a related p-local geometry"Mathematical Proceedings of the cambridge Philosophical Society. 133・3. 383-397 (2002)

泽部正人：“中心 p 根复形和相关的 p 局域几何”《剑桥哲学会数学会刊》133・3（2002 年）。