2010 Fiscal Year Final Research Report
Study on algebraic or combinatorial structures whose automorphism groups contain finite simple groups
| Project/Area Number |
19340002
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Chiba University |
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Principal Investigator |
KITAZUME Masaaki Chiba University, 大学院・理学研究科, 教授 (60204898)
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| 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)
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| Co-Investigator(Renkei-kenkyūsha) |
ABE Thoshiyuki 愛媛大学, 大学院・理工学研究科, 准教授 (30380215)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 有限群 / 符号 / デザイン / グラフ |
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| 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.
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