2000 Fiscal Year Final Research Report Summary
On the structure of a character ring of a finite group
| Project/Area Number |
11640010
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 |
YAMAUCHI Kenichi Chiba University, Faculty of Education, Associate Professor, 教育学部, 助教授 (20009690)
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| Co-Investigator(Kenkyū-buntansha) |
KITAZUME Masaaki Chiba University, Faculty of Science, Associate Professor, 理学部, 助教授 (60204898)
KOSHITANI Shigeo Chiba University, Faculty of Science, Professor, 理学部, 教授 (30125926)
NOZAWA Sohei Chiba University, Faculty of Science, Professor, 理学部, 教授 (20092083)
MARUYAMA Ken-ichi Chiba University, Faculty of Education, Associate Professor, 教育学部, 助教授 (70173961)
KOSHIKAWA Hiroaki Chiba University, Faculty of Education, Professor, 教育学部, 教授 (60000866)
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| Project Period (FY) |
1999 – 2000
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| Keywords | group / ring / field / representations of groups / modular representations of groups / irreducible character / character ring / irreducible Brauer character |
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| Research Abstract |
The objective of this research project is to study the structure of a chracter ring of a finite group. In the following we summarize our results.
First we studied the structure of the units group of a character ring of a finite group. Since the units of finite order in a chracter ring are well known, we considered the units of infinite order in a character ring. Actually we were able to construct units of infinite order in a character ring of a solvable group. We are going to write a paper on this result.
Secondly we studied induction theorems in ordinary representations of finite groups. By using Mackey decomposition theorem we have obtained another proof of a theorem of J.A.Green and written a paper. (K.Yamauchi, Another proof of a theorem of J.A.Green, Journal of Algebra 235 (2000), 829-832)
Thirdly we considered a generalization of a theorem of Weidman and Saksonov with respect to a Brauer character ring of a finite group. We have obtained useful and new results and written a paper. (K.Yamauchi, On isomorphisms of a Brauer character ring onto another, J.Alg. (to appear))
Finally we considered a generalization of a theorem of I.M.Isaacs about the extensions of representations of finite groups. We have obtained some new results and written a paper. (K.Yamauchi, On the Extensions of Group Representations over Arbitrary Fields II, The Bulletin of the Faculty of Education, Chiba Univerrsity 48 (2000), 11-19)
Other co-workers also have made contribution to this research project and obtained excellent results on their field as well.
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