2009 Fiscal Year Final Research Report
A computational study on extensions of algebraic number fields with non-commutative Galois groups
| Project/Area Number |
18540048
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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 | Sophia University |
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Principal Investigator |
TSUNOGAI Hiroshi Sophia University, 理工学部, 准教授 (20267412)
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| Co-Investigator(Kenkyū-buntansha) |
TSUZUKI Masao 上智大学, 理工学部, 准教授 (80296946)
UMEGAKI Atsuki 早稲田大学, 高等研究所, 准教授 (60329109)
MORIYAMA Tomonori 大阪大学, 理学研究科, 准教授 (80384171)
RIKUNA Yuuichi 早稲田大学, 理工学部, 講師 (10434309)
HOSHI Akinari 立教大学, 理学部, 助教 (50434262)
KOMATSU Tooru 東京理科大学, 理工学部, 講師 (10403974)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 整数論 / 代数学 / ガロア理論 / アルゴリズム |
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| Research Abstract |
Galois Theory is, shortly speaking, a theory of symmetry of numbers. Constructive Galois Theory aims at constructing prescribed symmetry explicitly. In this research, we have treated some cases with non-commutative Galois groups, and constructed explicit polynomials (mainly of degree 5 and 6) with featuring symmetry making use of geometric symmetry. It is significant that the polynomials have brief presentation so that we have obtained some number-theoretic properties.
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