2013 Fiscal Year Final Research Report
Research of the inverse Galois problems with restricted ramifications and their applications to the class field tower problems
| Project/Area Number |
23540010
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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 | Kanazawa University |
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Principal Investigator |
NOMURA Akito 金沢大学, 機械工学系, 教授 (00313700)
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| Co-Investigator(Kenkyū-buntansha) |
ITO Tatsuro 金沢大学, 数物科学系, 教授 (90015909)
HIRABAYASHI Mikihito 金沢工業大学, 基礎教育部, 教授 (20167612)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMADA Mieko 金沢大学, 数物科学系, 教授 (70130226)
KIMURA Iwao 富山大学, 理工学研究部, 准教授 (10313587)
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| Project Period (FY) |
2011 – 2013
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| Keywords | ガロアの逆問題 / 不分岐拡大 / 類体塔 / 類数 |
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| Research Abstract |
The main purpose of this research is to study the inverse Galois problems with restricted ramifications for p-groups and their applications to the class field tower problems.
Let p and q be distinct odd primes such that p-1 or p+1 is divisible by q. Let E be a non-abelian group of order p cubed, and let k be a cyclic extension over rational number field Q. We obtained the sufficient conditions for the existence of the unramified extension L/k such that the Galois group is isomorphic to E. By computing with PARI, we also gave some examples of cyclic fields which has an unramified extension with the Galois group E.
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