2003 Fiscal Year Final Research Report Summary
Applications of the classification of finite simple groups and prime graphs
| Project/Area Number |
14540034
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kumamoto University |
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Principal Investigator |
YAMAKI Hiroyoshi Kumamoto University, Graduate School of Natural Science, Professor, 大学院・自然科学研究科, 教授 (60028199)
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| Co-Investigator(Kenkyū-buntansha) |
IIYORI Nobuo Yamaguchi University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00241779)
ENDO Akira Kumamoto University, Faculty of Science, Associate Professor, 理学部, 助教授 (30032452)
WATANABE Atumi Kumamoto University, Faculty of Science, Professor, 理学部, 教授 (90040120)
SAWABE Masato Naruto University of Education, Faculty of Education, Research Assistant, 学校教育学部, 助手 (60346624)
CHIGIRA Naoki Muroran Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (40292073)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Finite simple groups / Prime graphs / p-local geometry |
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| Research Abstract |
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.
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