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Group Algebras and Code Theory

群代数和码论

基本信息

批准号：
11640003
负责人：
MOTOSE Kaoru
金额：
$ 2.24万
依托单位：
Hirosaki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640003/
关键词：
group algebra radical nilpotency Index finite Dickson near field Loewy series affine group cyclotomic polynomials code ルービー列有限半分配体群ルビー列 Near field Dickson near field 有限半分配体(near fields)Dickson near fields

项目摘要

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), 261-272H. 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.

给出了近域上仿射群的Loewy级数群代数的计算方法。下一篇论文是本文研究的基础。关于某些可解群的Loewy级数群代数，J.代数130(1990)，261-272H。Zassenhaus证明了有限近场是Dickson近场或七个例外近场。为了我们的目的，它需要知道近场的自同构。因此，我改进了H.Zassenous关于有限Dickson近场的自同构的证明。每个例外近场都不具有具有该近场特征的同阶自同构。因此，出于我们的目的，我们可能只考虑迪克森附近的场地。我研究了群代数的Loewy长度。我在会议上谈到了这项研究(詹姆斯·麦迪逊大学。(弗吉尼亚州哈里松堡)和研讨会(冈山大学，日本)。这些讲座的内容已在网站和会议记录中公布。我关于这方面的论文发表在《数学》杂志上。冈山大学。我们的目的还没有完成，但将在最近完成。我在会议上以《割圆多项式》为题，结合码和密码理论(Kyungpook NAT.韩国哥白尼大学)和波兰托伦哥白尼大学。