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Group Algebras and Code Theory

Research Project

Project/Area Number 11640003
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHirosaki University

Principal Investigator

MOTOSE Kaoru  Hirosaki University, Faculty of Science and Technology, Professor, 理工学部, 教授 (60020666)

Project Period (FY) 1999 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1999: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordsgroup algebra / radical / nilpotency Index / finite Dickson near field / Loewy series / affine group / cyclotomic polynomials / code / ルービー列 / 有限半分配体 / 群 / ルビー列 / Near field / Dickson near field / 有限半分配体(near fields) / Dickson near fields
Research Abstract

The purpose of this study is to make the method about computing Loewy series of group algebras of affine groups over near fields. The next my paper is a foundation for this study.
On Loewy series of group algebras of some solvable groups, J. Algebra 130 (1990), 261-272
H. Zassenhaus showed that finite near fields are Dickson near fields or seven exceptional near fields. It needs to know automorphisms of near fields for our purpose. So, I improved the proof of H. Zassenhous about automorphisms of finite Dickson near fields. Every exceptional near field has no automorphisms of the same order with the characteristic of this near field. Accordingly, we may consider only Dickson near fields for our purpose. I studied the Loewy length of a group algebra. I talk about this study in conference (James Madison Univ. (Harrisonburg, VA, USA) and symposium (Okayama University, Japan). Contents of these talks are published in web site and in Proceedings. My paper about this was published in Math. J. Okayama Univ. Our purpose is not completed but will be finished recently.
Concerning code and cipher theory, I talk in title "cyclotomic polynomials" at conference (Kyungpook Nat. Univ., Korea) and at Copernicus Univ., Torun, Poland.

Report

(5 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • Research Products

    (19 results)

All Other

All Publications (19 results)

  • [Publications] Kaoru Motose: "On commutative group algebras. III"Bull. Fac. Sci. Techn. Hirosaki Univ.. 1. 93-97 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kaoru Motose: "On values of cyclotomic polynomials"International Symposium on Ring Theory (Birkhauser). 231-234 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kaoru Motose: "On finite Dickson near fields"Bull. Fac. Sci. Techn. Hirosaki Univ. 2. 69-78 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kaoru Motose: "On nilpotency index of the radical of a group algebra. XI"Mathematical Journal of Okayama University. 44. 51-56 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kaoru Motose: "On values of cyclotomic polynomials V"Mathematical Journal of Okayama University. 45(印刷中). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kaoru Motose: "On the nilpotency index of the radical of a group algebra. XII"Bull. Fac. Sci. Techn. Hirosaki Univ. 6(印刷中). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 永原 賢, 本瀬 香: "代数的整数論入門"学術図書出版. 143 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Motose: "On commutative group algebras. III"Bull. Fac. Sci. Techn. Hirosaki Univ.. 1. 93-97 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Motose: "On values of cyclotomic polynomials"International Symposium on Ring Theory (Birkhauser). 231-234 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Motose: "On finite Dickson near fields"Bull. Fac. Sci. Techn. Hirosaki Univ.. 2. 69-78 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Motose: "On nilpotency index of the radical of a group algebra. XI"Math. J. Okayama Univ.. 44. 51-56 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Motose: "On values of cyclotomic polynomials V"Math. J. Okayama Univ.. 45, In press. (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Motose: "On the nilpotency index of the radical of a group algebra. XII"Bull. Fac. Sci. Techn. Hirosaki Univ.. 4, In press. (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Motose: "On Gauss sums and Vandermonde matrices"Bull. Fac. Sci. Techn. Hirosaki Univ.. 4, In press. (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kaoru Motose: "On the nilpotency index of the radical of a group algebra.XI"Math. J. Okayama Univ.. 44(印刷中). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kaoru Motose: "On the nilpotency index of the radical of a group algebra"Proc. 35-th Sympo. Ring Theory and Rep. Theory. 35. 161-164 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kaoru Motose: "On values of Cyclotomic Polynomials"International Symposium on Ring Theory. 論文集. 231-234 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kaoru Motose: "On Finite Dickson near fields"Bull.Fac.Sci.Hirosaki Unir.. 2. 69-78 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Motose: "On values of cyclotomic polynomials"Proc. of the third Korea-China-Japan International Symposium of Ring Theory, Birkhauser. 論文集. (2000)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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