Project/Area Number  09640046 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Algebra

Research Institution  Ehime University 
Principal Investigator 
SASAKI Hiroki Ehime University, Faculty of Science, Associate Professor, 理学部, 助教授 (60142684)

CoInvestigator(Kenkyūbuntansha) 
木曽 和啓 愛媛大学, 理学部, 教授 (60116928)
野倉 嗣紀 愛媛大学, 理学部, 教授 (00036419)
木村 浩 愛媛大学, 理学部, 教授 (70023570)
KISO Kazuhiro Ehime University, Faculty of Science, Prof.
KIMURA Hiroshi Ehime University, Faculty of Science, Prof.
NOGURA Tsugunori Ehime University, Faculty of Science, Prof.

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 1998 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1997 : ¥1,800,000 (Direct Cost : ¥1,800,000)

Keywords  finite groups / cohomology / representation theory / wreathed 2groups / extraspedal pgroups / 有限群 / コホモロジー論 / 表現論 / リース 2群 / エクストラスペシャルp群 / コホモロジー 
Research Abstract 
We proved some fundamental theorems which are useful to calculation of cohomology algebras of finite groups. Namely we showed a fact on vertices of Carlson modules, relations of projective covers relative to modules and Green correspondence, relations of Carlson modules and Green correspondence, and a construction of system of parameters from a productive class when prank is two, where p is a prime number. We constructed a module which appears in investigation of cohomology algebra of finite group G with Sylow psubgroup P such that (0) P has rank two (1) the center of P is cyclic (2) the centralizers of all elementary abelian subgroups of rank two are abelian and Sylow subgroups in the centralizers in G.Thereby the cohomology algebras of these finite groups can be investigated in a uniform way. As applications, first we calculated the mod 2 cohomology algebras of finite groups with wreathed Sylow 2subgroups. Second we studied mod p cohomology algebras of finite groups with extraspecial Sylow psubgroups of order p^3 and exponent p ; we constructed a general framework for the investigation. As an example we calculated the cohomology algebra of the general linear group GL(3, F_p), p > 3. Among such finite groups, the groups whose mod p cohomology algebras have been known are only Mathieu group M_<12> and GL(3, F_3) (these two finite groups have isomorphic cohomology algebras). We would be able to calculate cohomology algebras of sporadic finite simple groups with the same kind of Sylow psubgroups.
