2001 Fiscal Year Final Research Report Summary
Structure of finite simple groups and applications of the classification of finite simple groups
| Project/Area Number |
12640030
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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, Faculty of Science, Professor, 理学部, 教授 (60028199)
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| Co-Investigator(Kenkyū-buntansha) |
CHIGIRA Naoki Muroran Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (40292073)
ENDOU Akira Kumamoto University, Faculty of Science, Associate Professor, 理学部, 助教授 (30032452)
WATANABE Atumi Kumamoto University, Faculty of Science, Associate Professor, 理学部, 助教授 (90040120)
SAWABE Masato Kumamoto University, Faculty of Science, JSPS fellow, 理学部, 学振・PD
IIYORI Nobuo Yamaguchi University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00241779)
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| Project Period (FY) |
2000 – 2001
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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.
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.
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