Research on algebraic structures related to subgroup families of finite groups
| Project/Area Number |
25400006
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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 |
Sawabe Masato 千葉大学, 教育学部, 准教授 (60346624)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 有限群 / 単体複体 / ベキ零部分群 / クイバー / 部分群束 / パス代数 / 群指標 |
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| Outline of Final Research Achievements |
We regard a subgroup complex as a quiver. Then, by using the associated path algebra and its representation, we provide a new method for studying finite groups via subgroup complexes. Indeed, we introduce an integer called a generating constant from representations of path algebra, and applying those constants, we characterize finite solvable groups. In addition to this, we prove new properties of complex irreducible characters of finite groups. For further development on this research in the future, we focus on nilpotent subgroup complexes, and establish fundamental theory on homotopy and homology of such complexes.
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Report
(5 results)
Research Products
(14 results)
