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2000 Fiscal Year Final Research Report Summary

The inner meaning and classification of simplicial complexes admitting actions of groups

Research Project

Project/Area Number 09640035
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionOsaka Kyoiku University

Principal Investigator

YOSHIARA Satoshi  Fac.Education, Osaka Kyoiku University Professor, 教育学部, 教授 (10230674)

Co-Investigator(Kenkyū-buntansha) KITAMURA Kazuo  Fac.Education, Osaka Kyoiku University Professor, 教育学部, 教授 (30030381)
HIRAGI Akira  Fac.Education, Osaka Kyoiku University Lecturer, 教育学部, 講師 (90294181)
NAKAGAWA Nobuo  Kinki University Fac.Science & Tech.Assistant Professor, 理工学部, 助教授 (10088403)
ITO Tasuro  Kanazawa University Fac. Science Professor, 理学部, 教授 (90015909)
BABA Yoshitomo  Fac.Education, Osaka Kyoiku University Lecturer, 教育学部, 講師 (10201724)
Project Period (FY) 1997 – 2000
Keywordsradical subgroup / centric / EGQ / Y-family / dimensional dual hyperoval / semibiplane / Dade conjecture / homotopy equivalence
Research Abstract

The research of the head investigator on radical subgroups (Project(b)) clarifies the mathematical significance of the notion of centric radical subgroups, and shows the efficiency of some methods in algebraic topology to study group complexes. Furthermore, starting with the classification of group complexes of low rank (Part of Project(a)), he found new combinatorial objects, called Y-families and dimensional dual hyperovals, which can be thought of as higher dimensional analogues of quadrics in projective planes. His recent researches contribute to establish their importance as research subjects in finite geometry and combinatorics.
Further details on Project (a) : The notion of Y-families and dimensional dual hyperovals was found as well as the following machinery : their affine expansions give EGQ (extended generalized quadrangle)s and semibiplanes, which are complexes extending buildings and affine spaces of low rank. Motivated by the research of the head investigator, the classification of those objects has been now actively investigated as well as the related combinatorial objects, such as distance regular graphs.
On Project (b) : (l) It is now convincing that minimal complexes homotopically equivalent to those of chains of centric radical subgroups are main objects to investigate. Examinations of several examples by the head investigator contribute to the recent theory of Makoto Sawabe on homotopy equivalence which covers many classes of geometries. In future, many researches in this area will be devoted to generalizing his results.
(2) All radical subgroups of every sporadic simple groups except the Monster and the baby Monster for p=2 are determined.(In the exceptional cases, the results are believed to complete.) This gives the radical chains in many sporadic groups, and it makes possible to delete many chains unnecessary to examine for verifying the Dade conjecture.

  • Research Products

    (54 results)

All Other

All Publications (54 results)

  • [Publications] S.Yoshiara(with S.D.Smith): "Some homotopy equivalence for sporadic geometries"Journal of Algebra. 192. 326-379 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Yoshiara: "An example of non-isomorphic group association schemes with the same parameters"European Journal of Combinatorics. 18. 721-738 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Yoshiara: "On some flag-transitive non-classical c.C_2-geometries II"Contributions to Algebra and Geometry. 38. 357-375 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Yoshiara: "A construction of extended generalized quadrangles using the Veronesean"European Journal of Combinatorics. 18. 835-848 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Yoshiara: "The Borel-Tits property for finite groups"Groups and Geometnes, Siena Conference, Septembor 1996 Trends in Mathematics. 237-249 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Yoshiara: "The universal covers of a family of extended generalized quadrangles"European Journal of Combinatorics. 19. 753-765 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Hiraki: "Distance-regular subgraphs in a distance-regular graph, V"European Journal of Combinatorics. 19. 141-150 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Hiraki: "Distance-regular subgraphs in a distance-regular graph, VI"European Journal of Combinatorics. 19. 9-965 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Hiraki: "An application of a construction theory of strongly clased subgraphs in a distance-regular graph"European Journal of Combinatorics. 20. 271-278 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Hiraki: "Strongly closed subgraphs in a regular thick near polygon"European Journal of Combinatorics. 20. 789-796 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Hiraki: "Distance-regular graphs of the height h"Graphs and Combinatorics. 15. 417-428 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Hiraki: "Geodetically closed subgraphs in a distance-regular graph"Kyushi J.Mathematics. 54. 155-164 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Yoshiara: "A family of d-dimensional dual hyperovals in PG(2d+1,2)"European Journal of Combinatorics. 20. 589-603 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Yoshiara: "The radical 2-subgroups of the sporadic simple groups J_4, Co2 and Th"Journal of Algebra. 233. 309-341 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Yoshiara: "On a family of planes of a polar space"European Journal of Combinatorics. 22. 107-118 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Yoshiara: "Radical subgroups of the sporadic simple group of Suzuki"Advanced Studies in Pure Mathematics. to appear.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Nakagawa: "On strongly regular graphs with parameters (k,0,2) and theor antipodal double covers"Hokkaido Math.Journal. to appear.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Hiraki: "Distance-regular subgraphs in a distance-regular graph, N"European Journal of Combinatorics. 18. 635-645 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Hiraki: "Retracing argument for distance-regular graphs"J.Combinatorial Theory, Sev.B.. 79. 211-220 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Kitamura(with Y.Seo): "An inner characterization of the Hadamard product"Mathematica Japanica. 45. 211-216 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Kitamura(with Y.Seo): "Operation inequalities on Hadamard product associated with Kadison's Schwarz inequalities"Scientiae Mathematicae. 1. 237-241 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Kitamura(with R.Nakamoto): "Schwarz inequalities on Hadamard product"Scientiae Mathematicae. 1. 243-246 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Baba: "Some classes of QF-3 rings"communication in Algebra. 28. 2639-2669 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Baba: "On Harada rings and quasi-Harada rings with global dimension at most 2"Communication in Algebra. 28. 2671-2684 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Iro(with S.Hobart): "The structure of nonthin irreducible T-modules endpoint 1 : ladder bases and classical parameters."J.Algebraic Combinatorics. 7. 53-75 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Ito(with H.Ishibashi and M.Yamada): "Terwilliger algebras of cyclotomic schemes and Jacobi sums"European J.Combinatorics. 20. 397-410 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Ito(with K.Tanabe and P.Terwilliger): "Some algebra related to P- and Q-polynomial association schemes"DIMACS : Series in Discrete Mathematics and Theoretical Computer Science/BARG. (to apear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Yoshiara (with S.D.Smith): "Some homotopy equivalence for sporadic geometries"Journal of Algebra. 192. 326-379 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Yoshiara: "An example of non-isomorphic group association schemes with the same parameters"European J.of Combinatorics. 18. 721-738 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Yoshiara: "On some flag-transitive non-classical c.C_2-geometries II"Contributions to Algebra and Geometry. 38. 357-375 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Yoshiara: "A construction of extended generalized quadrangles using the Veronesean"European J.of Combinatorics. 18. 835-848 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Yoshiara: "The Borel-Tits property for finite groups"Groups and Geometries, Siena Conference, September 1996 Trends in Mathematics. 237-249 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Yoshiara: "The universal covers of a family of extended generalized quadrangles"European J.of Combinatorics. 19. 753-765 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Yoshiara: "A family of d-dimensional dual hyperovals in PG(2d+1,2)"European J.of Combinatorics. 20. 589-603 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Yoshiara: "The radical 2-subgroups of the sporadic simple groups J_4, Co2 and Th"Journal of Algebra. 233. 309-341 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Yoshiara: "On a family of planes of a polar space"European J.of Combinatorics. 22. 107-118 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Yoshiara: "Radical subgroups of the sporadic simple group of Suzuki"Advanced Studies in Pure Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N.Nakagawa: "On strongly regular graphs with parameters (k, 0,2) and their antipodal double covers"Hokkaido Math.Journal. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A.Hiraki: "Distance-regular subgraphs in a distance regular graph, IV"European J.of Combinatorics. 18. 635-645 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A.Hiraki: "Distance-regular subgraphs in a distance regular graph, V"European J.of Combinatorics. 19. 141-150 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A.Hiraki: "Distance-regular subgraphs in a distance regular graph, VI"European J.of Combinatorics. 19. 953-965 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A.Hiraki: "An application of a construction theory of strongly closed subgraphs in a distance-regular graph"European J.of Combinatorics. 20. 271-278 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A.Hiraki: "Strongly closed subgraphs in a regular thick near polygon"European J.of Combinatorics. 20. 789-796 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A.Hiraki: "Distance-regular graphs of the height h"Graphs and Combinatorics. 15. 417-428 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A.Hiraki: "Geodetically closed subgraphs in a distance-regular graph"Kyushu J.Mathematics. 54. 155-164 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A.Hiraki: "Retracing argument for distance-regular graphs"J.Combinatorial Theory, Ser.B. 79. 211-220 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Baba: "Some classes of QF-3 rings"Communications in Algebra. 28. 2639-2669 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Baba: "On Harada rings and quasi-Harada rings with left global dimension at most 2"Communications in Algebra. 28. 2671-2684 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kitamura (with Y.Seo): "An inner characterization of the Hadamard product"Mathematica Japonica. 45. 211-216 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kitamura (with Y.Seo): "Operator inequalities on Hadamard product associated with Kadison's Schwarz inequalities"Scientiae Mathematicae. 1. 237-241 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kitamura (with R.Nakamoto): "Schwarz inequalities on Hadamard product"Scientiae Mathematicae. 1. 243-246 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Ito (with S.Hobart): "The structure of nonthin irreducible T-modules of endpoint 1 : ladder bases and classical parameters"J.Algebraic Combinatorics. 7. 53-75 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Ito (wich H.Ishibashi and M.Yamada): "Terwillger algebras of cyclotomic schemes and Jacobi sums"European J.Combinatorics. 7. 397-410 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Ito (with K.Tanabe and P.Terwillger): "Some algebra related to P -and Q-polynomial association schemes"DIMACS : Series in Discrete Mathematics and Theoretical Computer Science/BARG. (to appear).

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

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Published: 2002-03-26  

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