Study of simple groups by subgroups structures and associated combinatrial structures

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540024
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kumamoto University
• Principal Investigator: CHIGIRA Naoki 熊本大学, 自然科学研究科, 准教授 (40292073)
• Co-Investigator(Renkei-kenkyūsha): WATANABE Atumi 熊本大学, 大学院自然科学研究科, 教授 (90040120) ; HIRAMNE Yutaka 熊本大学, 教育学部, 教授 (30116173) ; SHIROMOTO Keisuke 熊本大学, 大学院自然科学研究科, 教授 (00343666)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 単純群 / 組合せ構造

Outline of Final Research Achievements

We mainly studied the structure of the Rudvalis simple group, which is one of sporadic simple groups. Using a subgroup isomorphic to 3 dimensional unitary group over a field of 9 elements, we can construct a lattice in a 28 dimensional representation space over a complex field, and we can construct a monomial subgroup with respect to the canonical basis for the space. Using a subgroup of order 7 in the uinitary group, we had an orthonormal basis, which consists of minimal norm vectors in the lattice. And we constructed another monomial group with respect to the orthogona al basis. From these groups, we can find a generator of the Rudvalis group. We also construct various combinatorial structures using the lattice.

Free Research Field

代数学