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2004 Fiscal Year Final Research Report Summary

Homotopy equivalence and characterizations of subgroup complexes

Research Project

Project/Area Number 13640021
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Woman's Christian University (2003-2004)
Osaka Kyoiku University (2001-2002)

Principal Investigator

YOSHIARA Satoshi  Tokyo Woman's Christian University, Department of Mathematics, Professor, 文理学部, 教授 (10230674)

Co-Investigator(Kenkyū-buntansha) KOBAYASHI Kazuaki  Tokyo Woman's Christian University, Professor, 文理学部, 教授 (50031323)
OYAMA Nobuyuki  Tokyo Woman's Christian University, Professor, 文理学部, 教授 (80223981)
YAMASHIMA Shigeho  Tokyo Woman's Christian University, Associate Professor, 文理学部, 助教授 (80086347)
ISHIWATA Makiko  Tokyo Woman's Christian University, Instructor, 文理学部, 助手 (80277095)
SUGIYAMA Masumi  Tokyo Woman's Christian University, Instructor, 文理学部, 助手 (30086368)
Project Period (FY) 2001 – 2004
Keywordsdimensional dual hyperoval / radical subgroup / generalized quadrangle / Monster / Fischer groups / homotopy equivalence / classifying space / subgroup complex
Research Abstract

I obtained the following results to projects (A)(1)-(3) and (B).
(A)Research of extended buildings and the related combinatorial structures.
(A-1)Characterization of extensions of buildings of spherical type, without assuming group actions : For the automorphism group of a generalized quadrangles acting regularly on its point set, its structure is severely restricted.
(A-2)Determination of the universal embeddings of related complexes : Many results on dimensional dual hyperovals-embeddings of dual circle geometries-are obtained, for example, the best upper bound for dimensions of their ambient spaces, fundamental properties and examples of those with metric, construction of sub dual hyperovals as substructures fixed by automorphisms, calculation of automorphism groups of known examples, and solutions for isomorphism problem between them.
(A-3)Research on the related functions on finite fields : Characteristic functions exploited in the construction of dual hyperovals by Buratti and Del Fra are classified.
(B)Construction of theory for homotopy equivalences of complexes of centric radical p-subgroups and its applications : (1)My project of determining radical subgroups for all sporadic simple groups is completed by determining those for the Monster and Baby Monster. (2)I made a contribution to the project by S.D.Smith and D.Benson for explicitly constructing classifying space for each sporadic simple group (for the Fischer groups). (3)The highest dimension of non-vanishing homology groups of p-subgroup complexes is determined for each prime p.

  • Research Products

    (17 results)

All 2005 2004 2002 2001 Other

All Journal Article (17 results)

  • [Journal Article] Dimensional dual hyperovals associated with Steiner systems2005

    • Author(s)
      A.del Fra, S.Yoshiara
    • Journal Title

      European Journal of Combinatorics 26

      Pages: 173-194

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On dimensional dual hyperovals S^{d+1}_{sigma,phi}2005

    • Author(s)
      H.Taniguchi, S.Yoshiara
    • Journal Title

      Innovations in Invidence Geometry 1

      Pages: 197-219

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Radical 2-subgroups of the Monster and Baby Monster2005

    • Author(s)
      S.Yoshiara
    • Journal Title

      Journal of Algebra 287

      Pages: 123-139

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On dimensional dual hyperovals S^{d+1}_{sigma,phi}2005

    • Author(s)
      H.Taniguchi, S.Yoshiara
    • Journal Title

      Innovations in Incidence Geometry 1

      Pages: 197-219

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Ambient spaces of dimensional dual arcs2004

    • Author(s)
      S.Yoshiara
    • Journal Title

      Journal of Algebraic Combinatorics 19

      Pages: 5-23

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The radical 2-subgroups of some sporadic simple groups2002

    • Author(s)
      S.Yoshiara
    • Journal Title

      Journal of Algebra 248

      Pages: 237-264

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Dade's conjecture for the simple O'Nan group2002

    • Author(s)
      K.Uno, S.Yoshiara
    • Journal Title

      Journal of Algebra 249

      Pages: 147-185

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The radical subgroups of the Fischer simple groups2002

    • Author(s)
      M.Kitazume, S.Yoshiara
    • Journal Title

      Journal of Algebra 255

      Pages: 22-58

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On a family of planes of a polar space2001

    • Author(s)
      S.Yoshiara
    • Journal Title

      European Journal of Combinatorics 22

      Pages: 107-118

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On a new family of flag-transitive semibiplanes2001

    • Author(s)
      A.Pasini, S.Yoshiara
    • Journal Title

      European Journal of Combinatorics 22

      Pages: 529-545

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] New distance regular graphs arising from dimensional dual hyperovals2001

    • Author(s)
      A.Pasini, S.Yoshiara
    • Journal Title

      European Journal of Combinatorics 22

      Pages: 547-560

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Radical subgroups of the sporadic Suzuki simple group2001

    • Author(s)
      S.Yoshiara
    • Journal Title

      Advanced Studies in Pure Mathematics 32

      Pages: 453-464

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] New distance regular graphs arising from dimensional dual hyperovals2001

    • Author(s)
      B.Pasini, S.Yoshiara
    • Journal Title

      European Journal of Combinatorics 22

      Pages: 547-560

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A generalized quadrangle with an automorphism group acting regularly on the points

    • Author(s)
      S.Yoshiara
    • Journal Title

      European Journal of Combinatorics To appear

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Some remarks on dimensional dual hyperovals of polar type

    • Author(s)
      S.Yoshiara
    • Journal Title

      Bulletin of Belgian Mathematical Society - Simon Stevin To appear

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A generalized quadrangle with an automorphism group acting regularly on the points

    • Author(s)
      S.Yoshiara
    • Journal Title

      European Journal of Combinatorics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Some remarks on dimensional dual hyperovals of polar type

    • Author(s)
      S.Yoshiara
    • Journal Title

      Bulletin of Belgian Math.Society-Simon Stevin (to appear)

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

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Published: 2006-07-11  

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