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Subgroup complexes of finite groups, and their representation and geometry

Research Project

Project/Area Number 19740005
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionChiba University

Principal Investigator

SAWABE Masato  Chiba University, 教育学部, 准教授 (60346624)

Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,040,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥540,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥700,000 (Direct Cost: ¥700,000)
Keywords群論 / 一般バーンサイド環 / 部分群複体 / 有限群 / レフシェッツ不変量 / 根基部分群 / レフシェッツ加群 / 非中心的根基部分群
Research Abstract

In order to study the structure theory of finite groups, it is quite important to investigate that how various subgroups of the group relate or intersect each other. Then we consider an abstract simplicial complex defined by inclusion chains of subgroups as simplices ; which is called "subgroup complex". We obtained some results on the Lefschetz module, the generalized Burnside ring, or the homotopy invarinat associated to subgroup complexes.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (15 results)

All 2011 2009 2008 2007

All Journal Article (8 results) (of which Peer Reviewed: 8 results) Presentation (7 results)

  • [Journal Article] The generalized Burnside rings with respect to a collection of self-normalizing subgroups.2011

    • Author(s)
      Fumihito Oda, Masato Sawabe
    • Journal Title

      Journal of Algebra 掲載予定

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The generalized Burnside rings with respect to a collection of self-normalizing subgroups2011

    • Author(s)
      Fumihito Oda, Masato Sawabe
    • Journal Title

      Journal of Algebra

      Volume: 334 Pages: 219-231

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A collection of subgroups for the generalized Burnside ring.2009

    • Author(s)
      Fumihito Oda, Masato Sawabe
    • Journal Title

      Advances in Mathematics 222巻

      Pages: 307-317

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A collection of subgroups for the generalized Burnside ring.2009

    • Author(s)
      Fumihito Oda, Masato Sawabe
    • Journal Title

      Advances in Mathematics 222

      Pages: 307-317

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A collection of subgroups for the generalized Burnside ring2009

    • Author(s)
      Fumihito Oda, Masato Sawabe
    • Journal Title

      Advances in Mathematics 222

      Pages: 307-317

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on finite simple groups with abelian Sylow p-subgroups.2007

    • Author(s)
      Masato Sawabe
    • Journal Title

      Tokyo Journal of Mathematics 30巻

      Pages: 293-304

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on finite simple groups with abelian Sylow p-subgroups.2007

    • Author(s)
      Masato Sawabe
    • Journal Title

      Tokyo Journal of Mathematics 30

      Pages: 293-304

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A note on finite simple groups with abelian Sylow p-subgroups2007

    • Author(s)
      Masato Sawabe
    • Journal Title

      Tokyo Journal of Mathematics 30

      Pages: 293-304

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] A collection of subgroups for the generalized Burnside ring2009

    • Author(s)
      澤邉正人
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2010 Final Research Report 2009 Annual Research Report 2009 Self-evaluation Report
  • [Presentation] 一般バーンサイド環のための新たな部分群の族2009

    • Author(s)
      澤邉正人
    • Organizer
      有限群のコホモロジー論とその周辺
    • Place of Presentation
      信州大学
    • Year and Date
      2009-09-02
    • Related Report
      2010 Final Research Report 2009 Annual Research Report 2009 Self-evaluation Report
  • [Presentation] A collection of subgroups for the generalized Burnside ring2009

    • Author(s)
      小田文仁、澤邉正人
    • Organizer
      第26回代数的組合せ論シンポジウム
    • Place of Presentation
      山形大学
    • Year and Date
      2009-06-25
    • Related Report
      2010 Final Research Report 2009 Annual Research Report 2009 Self-evaluation Report
  • [Presentation] ある種の一般バーンサイド環について2009

    • Author(s)
      澤邉正人
    • Organizer
      群論セミナー
    • Place of Presentation
      熊本大学
    • Year and Date
      2009-03-05
    • Related Report
      2008 Annual Research Report
  • [Presentation] ある部分群族と一般バーンサイド環について2009

    • Author(s)
      澤邉正人
    • Organizer
      有限群論駒場セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2009-02-02
    • Related Report
      2008 Annual Research Report
  • [Presentation] A family for the partial Burnside ring of the Monster and its Reduced Euler characteristic2008

    • Author(s)
      澤邉正人
    • Organizer
      群論セミナー
    • Place of Presentation
      北海道大学理学部
    • Year and Date
      2008-10-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] The centric p-radical subgroups and the reduced Lefschetz module2008

    • Author(s)
      澤邉正人
    • Organizer
      Groups and Combinatorics seminar
    • Place of Presentation
      北海道大学理学部
    • Year and Date
      2008-06-20
    • Related Report
      2008 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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