• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Study on algebraic or combinatorial structures whose automorphism groups contain finite simple groups

Research Project

Project/Area Number 19340002
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

KITAZUME Masaaki  Chiba University, 大学院・理学研究科, 教授 (60204898)

Co-Investigator(Kenkyū-buntansha) NOZAWA Sohei  千葉大学, 大学院・理学研究科, 教授 (20092083)
KOSHITANI Shigeo  千葉大学, 大学院・理学研究科, 教授 (30125926)
SAWABE Masato  千葉大学, 教育学部, 准教授 (60346624)
SUGIYAMA KenーIchi  千葉大学, 大学院・理学研究科, 教授 (90206441)
ANDO Tetsuya  千葉大学, 大学院・理学研究科, 准教授 (20184319)
YAMADA Hiromichi  一橋大学, 大学院・経済学研究科, 教授 (50134888)
MUNEMASA Akihiro  東北大学, 大学院・情報科学研究科, 教授 (50219862)
HARADA Masaaki  山形大学, 理学部, 准教授 (90292408)
CHIGIRA Naoki  熊本大学, 大学院・自然科学研究科, 准教授 (40292073)
Co-Investigator(Renkei-kenkyūsha) ABE Thoshiyuki  愛媛大学, 大学院・理工学研究科, 准教授 (30380215)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000)
Fiscal Year 2010: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2009: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2008: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2007: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Keywords有限群 / 符号 / デザイン / グラフ / 単純群 / 散在型単純群 / 格子 / 頂点作用素代数
Research Abstract

We have studied some algebraic structures and combinatorial structured whose automorphism groups contain finite simple groups.
(1) We have studied the binary code spanned by the sets of fixed points of the involutions of a finite transitive permutation group and its dual code. New self-dual codes invariant under the Hall-Janko group and the Rudvalis group have been constructed, respectively.
(2) We have studied rank 3 graphs related to some sporadic simple groups (especially, HJ, Suz, M24). New constructions of these rank 3 graphs from some designs have been obtained.
(3) We have determined the minimum value m such that a given Niemeier lattice is a m-neighbor of the Leech lattice.

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

    (21 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (12 results) (of which Peer Reviewed: 12 results) Presentation (8 results) Remarks (1 results)

  • [Journal Article] On the maximum coclique of the rank 3 graph of 2^<11>:M_<24>2009

    • Author(s)
      N.Horiguchi, M.Kitazume, H.Nakasora
    • Journal Title

      Journal of Combinatorial Designs 17

      Pages: 323-332

    • Related Report
      2010 Final Research Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A construction of the sporadic Suzuki graph from U_3(4)2009

    • Author(s)
      A.E.Brouwer, N.Horiguchi, M.Kitazume, H.Nakasora
    • Journal Title

      Journal of Combinatorial Theory (A) 116

      Pages: 1009-1096

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the maximum coclique of the rank 3 graph of 2^<11>:M_<24>2009

    • Author(s)
      N. Horiguchi, M. Kitazume, H. Nakasora
    • Journal Title

      Journal of Combinatorial Designs 17

      Pages: 323-332

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A construction of the sporadic Suzuki graph from U_3(4)2009

    • Author(s)
      A. E. Brouwer, N. Horiguchi, M. Kitazume, H. Nakasora
    • Journal Title

      Journal of Combinatorial Theory (A) 116

      Pages: 1009-1096

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A construction of the sporadic Suzuki graph from U_3(4)2009

    • Author(s)
      A.E.Brouwer, N.Horiguchi, M.Kitazume, H.Nakasora
    • Journal Title

      Journal of Combinatorial Theory(A) 116

      Pages: 1009-1096

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Hall-Janko graph and the Witt system W_<10>2008

    • Author(s)
      N.Horiguchi, M.Kitazume, H.Nakasora
    • Journal Title

      European Journal of Combinatorics 29

      Pages: 1-8

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Hall-Janko graph and the Witt system W_102008

    • Author(s)
      N. Horiguchi, M. Kitazume, H. Nakasora
    • Journal Title

      European Journal of Combinatorics 29

      Pages: 1-8

    • Related Report
      2009 Self-evaluation Report 2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some Self-Dual Codes Invariant under the Hall-Janko Group2007

    • Author(s)
      N.Chigira, M.Kitazume, M.Harada
    • Journal Title

      Journal of Algebra 316

      Pages: 578-590

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Some Self-Dual Codes Invariant under the Hall-Janko Group2007

    • Author(s)
      N. Chigira, M. Harada, M. Kitazume
    • Journal Title

      Journal of Algebra 316

      Pages: 578-590

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some Self-Dual Codes Invariant under the Hall-Janko Group

    • Author(s)
      N. Chigira, M. Kitazume, M. Harada
    • Journal Title

      Journal of Algebra 316

      Pages: 578-590

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On the maximum coclique of the rank 3 graph of 211. M24

    • Author(s)
      N. Horiguchi, M. Kitazume, H. Nakasora
    • Journal Title

      Journal of Combinatorial Designs (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A construction of the sporadic Suzuki graph from U3(4)

    • Author(s)
      N. Horiguchi, M. Kitazume, H. Nakasora
    • Journal Title

      Journal of Combinatorial Theory (A) (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Co 3をめぐって2011

    • Author(s)
      北詰正顕
    • Organizer
      有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2011-08-01
    • Related Report
      2010 Annual Research Report
  • [Presentation] Co_3をめぐって2010

    • Author(s)
      北詰正顕
    • Organizer
      第22回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス
    • Related Report
      2010 Final Research Report
  • [Presentation] Neighbors of the Leech lattice2010

    • Author(s)
      北詰正顕
    • Organizer
      ミニ集会「代数的組合せ論」
    • Place of Presentation
      神戸学院大学
    • Related Report
      2010 Final Research Report 2009 Annual Research Report 2009 Self-evaluation Report
  • [Presentation] 散在型単純群の周辺2009

    • Author(s)
      北詰正顕
    • Organizer
      第53回代数学シンポジウム
    • Place of Presentation
      盛岡市
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] 単純群論の最近の話題とこれからの課題2009

    • Author(s)
      北詰正顕
    • Organizer
      第21回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス
    • Related Report
      2010 Final Research Report
  • [Presentation] 散在型単純群の周辺2008

    • Author(s)
      北詰正顕
    • Organizer
      第53回代数学シンポジウム
    • Place of Presentation
      盛岡市アイーナ
    • Year and Date
      2008-08-08
    • Related Report
      2008 Annual Research Report
  • [Presentation] DicksonのE_6(q)2008

    • Author(s)
      北詰正顕
    • Organizer
      第20回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス
    • Related Report
      2010 Final Research Report
  • [Presentation] Hall Janko graphについて2007

    • Author(s)
      北詰正顕
    • Organizer
      第19回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス
    • Related Report
      2010 Final Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.math.s.chiba-u.ac.jp/~kitazume/

    • Related Report
      2010 Final Research Report

URL: 

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

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi