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2003 Fiscal Year Final Research Report Summary

Inverse Galois Problems with Restricted Ramifications

Research Project

Project/Area Number 14540018
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKANAZAWA 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
Keywordsembedding 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)

All Other

All Publications (16 results)

  • [Publications] A.Nomura: "A note on unramified quaternion extensions over quadratic number fields"Proc.Japan Acad.. 78. 80-82 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Nomura: "Notes on the existence of certain unramified 2-extensions"Illinois Journal of Math.. 46・4. 1279-1286 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Ito: "The shape of a tridiagonal pair"Journal of Pure and Applied Algebra. 印刷中.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Morishita: "On certain analogies between knots and primes"J.reine angew.Math.. 550. 141-167 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Morishita: "Milnor invariants and Massey products for prime numbers"Compositio Math.. 140. 69-83 (2004)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Fujisaki: "On Distributions of Multiple Access Interference for Spread Spectrum Communication System Using M-phase Spreading Sequence of Markov Chains"Proceedings of The 26^<th> Symposium on Information Theory and its Aplications. 26・2. 433-436 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Nomura: "A note on unramified quaternion extensions over quadratic number fields"Proc.Japan Acad.. vol.78. 80-82 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A.Nomura: "Notes on the existence of certain unramified 2-extensions"Illinois Journal of Math.. vol.46. 1279-1286 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Ito: "The shape of a tridiagonal pair"Journal of Pure and Applied Algebra. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Ito: "Designs in a coset geometry : Delsarte theory revisited"Europ.J.of Combinatorics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Morishita: "On certain analogies between knots and primes"J.reine angew.Math.. vol.550. 141-167 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Morishita: "On capitulation problem for 3-manifolds"Developments in Mathematics. vol.11. 305-313 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Morishita: "Milnor invariants and Massey products for prime numbers"Compositio Math.. vol.140. 69-83 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujisaki: "On Correlation Values of M-Phase Spreading Sequences of Markov Chains"IEEE Trans.on Circuit and Systems. vol.CAS49. 1745-1750 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujisaki: "Statistical Properties of Real-Valued Sequences of Generated by Chebyshev Maps"IEICE Transactions. vol.E85-A. 2003-2008 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujisaki: "On Distributions of Multiple Access Interference for Spread Spectrum Communication System Using M-phase Spreading Sequence of Markov Chains"Proceedings of The 26^<th> Symposium on Information Theory and its Applications. vol.26. 433-436 (2003)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2005-04-19  

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