2003 Fiscal Year Final Research Report Summary
Inverse Galois Problems with Restricted Ramifications
| Project/Area Number |
14540018
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | KANAZAWA UNIVERSITY |
|---|
Principal Investigator |
NOMURA Akito Kanazawa University, Faculty of Engineering, Assistant Professor, 工学部, 講師 (00313700)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
FUJISAKI Hiroshi Kanazawa University, Graduate School of Natural Science and Technology, Assistant Professor, 自然科学研究科, 講師 (80304757)
MORISHITA Masanori Kanazawa University, Faculty of Science, Associate Professor, 理学部, 助教授 (40242515)
ITO Tatsuro Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (90015909)
|
|---|
| Project Period (FY) |
2002 – 2003
|
| Keywords | embedding problem / unramified extension / class number / class field tower / inverse Galois problem |
|---|
| Research Abstract |
Our research results are summarized as follows. Head investigator Nomura studied the unramified solution of embedding problems and the existence of unramified p-extensions. One of main results in case when p is an odd prime is stated as follows. Let G be the group such that the GAP-number is[243,65], which is a non-abelian 3-group of order 243. If the class number of quintic cyclic fields F is divisible by 3,then there exists an unramified Galois extension over F such that the Galois group is isomorphic to G. In particular, the class number of the Hilbert class field of F is divisible by 3. In case when p=2,we also studied the existence of unramified quaternion extension over cyclic fields, and gave an affirmative answer of a special case of Fontaine-Mazur-Boston conjecture concerning the Galois group of class field tower.
Investigator Morishita discussed some analogies for primes coming from link theory, based on an analogy between the structure of the group of a link and those of certain Galois group. He also gave a cohomological interpretation of Redei's symbol by using refined Milnor invariants, and generalized a classical results of Redei concerning the ideal class group of quadratic fields.
|
Research Products
(16 results)
