| Project/Area Number |
12640021
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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 | Aichi University of Education |
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Principal Investigator |
HAYASHI Makoto (2001-2002) Aichi Univ.of Edu.Fac.of Edu.P, 教育学部, 教授 (40109369)
田原 賢一 (2000) 愛知教育大学, 教育学部, 教授 (00024026)
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| Co-Investigator(Kenkyū-buntansha) |
YASUMOTO Taichi Aichi Univ.of Edu.Fac.of Edu.AP, 教育学部, 助教授 (00231647)
WATANABE Osamu Aichi Univ.of Edu.Fac.of Edu.P, 教育学部, 教授 (30024011)
KANEMITSU Mitsuo Aichi Univ.of Edu.Fac.of Edu.P, 教育学部, 教授 (60024014)
KAWAMOTO Naoki Japan Coast Guard Acad.P, 教授
NINOMIYA Yasushi Shinshu Univ.Fac.of Sci.P, 理学部, 教授 (40092887)
古川 徹 山陽学園大学, 国際分化学部, 助教授 (40249537)
関口 勝右 国士館大学, 工学部, 助教授 (20146749)
林 誠 愛知教育大学, 教育学部, 教授 (40109369)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2002: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2001: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2000: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | radical / nilpotency indices / p-solvable group / Witt type Lie algebra / oversemigroup / devided semigroup / closure / Witt type Lie algehra / divided semigroup / 整群環 / Lisp / Witt algebra / Seminovmal semigroup / Riemenn-Roch-Weil / closure of a 2-group / 次元部分群問題 / 一般次元部分群問題 / 添加イテアル |
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| Research Abstract |
Let t be a nonnegative integer, S be a finite 2-group and U be an elementary abelian normal subgroup of S. We write U ∈ μ_t(S) if U = <u ; |[u, A]| 【less than or equal】 2^t> for any elementary abelian subgroup A of S with [U, A, A] = 1. Let G be a finite group, S ∈ Syl_2(G) and V = <u^q ; u ∈ U, g ∈G>. Hayashi gave an estimation of m such that V ∈ μ_m(S) whenever V is abelian. Let k be a field of characteristic p>0 and G be a finite group. The nilpotency index t(G) of the Jacobson radical of the group algebra k[G] is one of the most important invariant to investigate the group algebra. Let G be a finite p-solvable group, P ∈ Syl_p (G) and p^m =|P|. Ninomiya classified all the groups satisfying p^<m-2> < t(G) < p^<m-1>. Moreover, when p = 3, he gave the example group with t(G) > t(P). This is a counterexample to the conjecture that t(G) 【less than or equal】 t(P) always holds. Kawamoto proved that there is a duality between the simplicity of commutative associative algebras and its derivation Lie algebras under some suitable conditions. Knemitsu gave a necessary and sufficient condition that an oversemigroup of a torsion-free cancellative semigroup S is flat over 5. Let G be a torsionfree additive group and S be a submonoid of G. He proved that If S is a GCD-semigroup which has prime ideals that are linearly ordered, then S is a valuation semigroup.
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