| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Outline of Final Research Achievements |
We mainly studied the structure of the Rudvalis simple group, which is one of sporadic simple groups. Using a subgroup isomorphic to 3 dimensional unitary group over a field of 9 elements, we can construct a lattice in a 28 dimensional representation space over a complex field, and we can construct a monomial subgroup with respect to the canonical basis for the space. Using a subgroup of order 7 in the uinitary group, we had an orthonormal basis, which consists of minimal norm vectors in the lattice. And we constructed another monomial group with respect to the orthogona al basis. From these groups, we can find a generator of the Rudvalis group. We also construct various combinatorial structures using the lattice.
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