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2005 Fiscal Year Final Research Report Summary

The structure of a finite simple group and prime graphs

Research Project

Project/Area Number 16540030
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

YAMAKI Hiroyoshi  Kumamoto University, Graduate School of Science and Technology, Professor, 大学院・自然科学研究科, 教授 (60028199)

Co-Investigator(Kenkyū-buntansha) WATANABE Atumi  Kumamoto University, Faculty of Science, Professor, 理学部, 教授 (90040120)
HIRAMINE Yutaka  Kumamoto University, Faculty of Education, Professor, 教育学部, 教授 (30116173)
IIYORI Nobuo  Yamaguchi University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00241779)
CHIGIRA Naoki  Muroran Institute of technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (40292073)
SAWABE Masato  Naruto University of Education, Faculty of Education, Research Assistant, 学校教育学部, 助手 (60346624)
Project Period (FY) 2004 – 2005
KeywordsFinite simple group / Relative difference sets / Codes
Research Abstract

We studied about the structure of finite simple groups and found several properties of finite groups using the classification of finite simple groups and prime graphs.
Hiroyoshi Yamaki proved that if G is a group of even order and is not 2-rank 1, then there exists an involution t in G such that the order G is bounded by the cube of the order of the centralizer t in G.
Yutaka Hiramine studied about difference and relative difference sets for non- abelian groups. Especially Hiramine proved that there exists exactly two relative difference sets in the alternating group on 5 letters. Further more Hiramine constructed relative difference sets in dihedral groups.
Naoki Chigira, Masaaki Kitazume and Masaaki Harada constructed self dual code such that the 2^<nd> Janko group acts as automorphism group. Naoki Chigira gave an elementary construction of the Mathieu groups on 11 and 12 letters.
Nobuo Iiyori studied prime graphs and solvable graphs of finite groups and defined Burn side ring. Using these it has been proved that we can describe on the connectedness of the solvable graph by the properties of ideals on Burnside ring.
Masato Sawabe proved that the reduced Lefschetz module of the G-poset consisting of all centric p-radical subgroups of a finite group G is X-projective virtual Zp[G]-module where X is a family of p-subgroups of the normalizers of non-centric p-radical subgroups of G.

  • Research Products

    (12 results)

All 2006 2005

All Journal Article (12 results)

  • [Journal Article] On the reduced Lefschetz module and the centric p-radical subgroups, II2006

    • Author(s)
      澤辺 正人
    • Journal Title

      Journal of the London Mathematical Society 印刷中

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On left Hadamard transversals in non-solvable groups2006

    • Author(s)
      平峰 豊
    • Journal Title

      Discrete Mathematics 印刷中

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On relative difference sets in dihedral groups2006

    • Author(s)
      平峰 豊
    • Journal Title

      Designs, Codes and Cryptography 印刷中

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On the reduced Lefschetz module and the centric p-radical subgroups, II2006

    • Author(s)
      Masato Sawabe
    • Journal Title

      Journal of the London Mathematical Society (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On left Hadamard transversals in non-solvable groups2006

    • Author(s)
      Yutaka Hiramine
    • Journal Title

      Discrete Mathematics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On relative difference sets in dihedral groups2006

    • Author(s)
      Yutaka Hiramine
    • Journal Title

      Design, Codes and Cryptography (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Relative difference sets in Alt(5)2005

    • Author(s)
      平峰 豊
    • Journal Title

      Journal of Combinatorial Theory 110

      Pages: 179-191

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On perfect isometries for blocks with abelian defect groups and cyclic hyperfocal subgroups2005

    • Author(s)
      渡邉 アツミ
    • Journal Title

      Kumamoto Journal of Mathematics 18

      Pages: 85-92

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On the reduced Lefschetz module and the centric p-radical subgroups2005

    • Author(s)
      澤辺 正人
    • Journal Title

      Tokyo Journal of Mathematics 28・1

      Pages: 79-90

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On the reduced Lefschetz module and the centric p-radical subgroups2005

    • Author(s)
      Masato Sawabe
    • Journal Title

      Tokyo Journal of Mathematics 28

      Pages: 79-90

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On perfect isometries for blocks with abelian defect groups and cyclic hyperfocal subgroups2005

    • Author(s)
      Atumi Watanabe
    • Journal Title

      Kumamoto Journal of Mathematics 18

      Pages: 85-92

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Relative difference sets in alt(5)2005

    • Author(s)
      Yutaka Hiramine
    • Journal Title

      Journal of Combinatorial Theory 110

      Pages: 179-191

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

URL: 

Published: 2007-12-13  

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