| Co-Investigator(Kenkyū-buntansha) |
HIRAIDE Kouichi Faculty of Science, Ehime University, Associate Professor, 理学部, 助教授 (50181136)
KISO Kazuhiro Faculty of Science, Ehime University, Professor, 理学部, 教授 (60116928)
NOGURA Tsugunori Faculty of Science, Ehime University, Professor, 理学部, 教授 (00036419)
NIWASAKI Takashi Faculty of Science, Ehime University, Instructor, 理学部, 助手 (50218252)
SHAKHMATOV Dmitri Faculty of Science, Ehime University, Professor, 理学部, 教授 (90253294)
|
|---|
| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2001: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2000: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1999: ¥1,000,000 (Direct Cost: ¥1,000,000)
|
|---|
| Research Abstract |
As a continuation of our research on mod p cohomology algebras of finite groups with extraspecial Sylow p-subgroups, which was done under Grant-in-Aid for Scientific Research during 1997〜1998 (project number 096400460), we calculated the mod 7 cohomolgy algebra of Held simple group. In this work we completed the theoreical frame work on the cohomology algebras of finite groups of this kind. We also calculated the mod p cohomology algebra of the special linear group of degree 3 over the prime field of characteristic p.
We improved a theorem of Carlson on system of parameters. Namely if a finite group G has p-rank r, then the mod p cohomology algebra has a system of parameters ζ_1,...,ζ_r with the following properties: (1) for each i = 1,...,r, the element ζ_i is a sum of transfers from the centralizers of elementary abelian p=subgrpups of rank i; (2) for each i = 1,...,r, the restriction of {ζ_1,...,ζ_i} to an elementary abelian p-subgroup of rank i is a system of paramters of the cohomology algebra of this elementary abelian p-subgroup. From this fact we, in particular, showed that if a finite group G has p-rank less than or equal to 3, then the trivival kG-module k has index zero.
Using transfer maps of extension groups introduced by Carlson, Peng, Wheeler, we showed that an element ρ in the mod p cohomology algebra of a finite group G is regular if and only if the transfer map Tr^<L_p> : Ext^*_<kG>(L_ρ,L_ρ) → Ext^*_<kG>, (k,k) defined by the Carlson module L_ρ is the zero map. Relating to this result we proved that if a finitely generated kG-module W is protective over a cyclic shifted subgroup in the center of a Sylow p-subgroup, then the transfer map Tr^W : Ext^*_<kG>(W,W) → Ext^*_<kG>(k,k) defined by the module W is the zero map.
|
