| 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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| 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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