Various aspects of sporadic simple groups

2017 Fiscal Year Final Research Report

• Project/Area Number: 24340002
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Chiba University
• Principal Investigator: KITAZUME MASAAKI 千葉大学, 大学院理学研究院, 教授 (60204898)
• Co-Investigator(Renkei-kenkyūsha): SAWABE Masato 千葉大学, 教育学部, 准教授 (60346624) ; MUNEMASA Akihiro 東北大学, 大学院情報科学研究科, 教授 (50219862) ; CHIGIRA Naoki 熊本大学, 大学院先端科学研究部, 准教授 (40292073) ; HARADA Masaaki 東北大学, 大学院情報科学研究科, 教授 (90292408) ; ABE Toshiyuki 愛媛大学, 教育学部, 教授 (30380215) ; SHIMAKURA Hiroki 東北大学, 大学院情報科学研究科, 准教授 (90399791)
• Research Collaborator: NAKASORA Hiroyuki ; HORIGUCHI Naoyuki ; IRIE Yuuki ; KOBAYASHI Yusuke
• Project Period (FY): 2012-04-01 – 2018-03-31
• Keywords: 有限群 / 散在型単純群 / 符号 / 格子 / グラフ / デザイン

Outline of Final Research Achievements

We have studied the Rudvalis simple group and related algebraic structures (code, lattice) and combinatorial structure (graph, design). Consequently we show the existence of even self-dual code preserved by the Rudvalis group, and give a combinatorial description of some generator. We further define five 2-designs by using a unitary group, and give a new construction of the Rudvalis graph from these 2-designs. We also consider Conway's theorem, which show the relation between the Rudvalis graph and the Hoffman-Singleton graph.
Moreover we have completed the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups by showing non-existence of the remaining case.

Free Research Field

群論，代数的組合せ論