2002 Fiscal Year Final Research Report Summary
Group Algebras and Code Theory
| Project/Area Number |
11640003
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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 | Hirosaki University |
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Principal Investigator |
MOTOSE Kaoru Hirosaki University, Faculty of Science and Technology, Professor, 理工学部, 教授 (60020666)
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| Project Period (FY) |
1999 – 2002
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| Keywords | group algebra / radical / nilpotency Index / finite Dickson near field / Loewy series / affine group / cyclotomic polynomials / code |
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| Research Abstract |
The purpose of this study is to make the method about computing Loewy series of group algebras of affine groups over near fields. The next my paper is a foundation for this study.
On Loewy series of group algebras of some solvable groups, J. Algebra 130 (1990), 261-272
H. Zassenhaus showed that finite near fields are Dickson near fields or seven exceptional near fields. It needs to know automorphisms of near fields for our purpose. So, I improved the proof of H. Zassenhous about automorphisms of finite Dickson near fields. Every exceptional near field has no automorphisms of the same order with the characteristic of this near field. Accordingly, we may consider only Dickson near fields for our purpose. I studied the Loewy length of a group algebra. I talk about this study in conference (James Madison Univ. (Harrisonburg, VA, USA) and symposium (Okayama University, Japan). Contents of these talks are published in web site and in Proceedings. My paper about this was published in Math. J. Okayama Univ. Our purpose is not completed but will be finished recently.
Concerning code and cipher theory, I talk in title "cyclotomic polynomials" at conference (Kyungpook Nat. Univ., Korea) and at Copernicus Univ., Torun, Poland.
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