| Project/Area Number |
17K05161
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Chiba University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 有限群 / 単体複体 / 表現論 / ポセット / 半順序集合 / 指数 / 表現 / 部分群複体 / ホモロジー / 類関数 / 群複体 |
|---|
| Outline of Final Research Achievements |
A family of subgroups of a finite group can be regarded as a partially ordered set, an order complex, or a quiver with respect to the inclusion relation among the subgroups. First, we determined the homology group of the complex of non-trivial nilpotent subgroups of a finite non-solvable group. Second, we proposed the quiver representation associated to the complex of the totality of subgroups, and developed the basis for it. Third, we introduced the concept of d-cover for a certain complex of nilpotent subgroups, and in particular we characterized 1-cover. In addition, we proved the group-theoretic nature derived from the 2-cover.
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| Academic Significance and Societal Importance of the Research Achievements |
世の中のあらゆるところに存在する対称性を抽象化した数学的対象は群と呼ばれる。群はある種の代数系であるが、群が有する沢山の部分群におけるその配置を幾何学的に考察し、その情報を元の群の性質にフィードバックさせることが本研究の特徴である。学術的に本研究成果は有限単純群の統一的理解への示唆を与えるものである。また社会的は一般的な対称性の数学的理解を与えるものである。
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