广义Dedekind定理及其在整数群行列式中的应用

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of the Mathematical Society of Japan Pub Date : 2023-11-01 DOI:10.2969/jmsj/90539053

Naoya YAMAGUCHI, Yuka YAMAGUCHI

{"title":"广义Dedekind定理及其在整数群行列式中的应用","authors":"Naoya YAMAGUCHI, Yuka YAMAGUCHI","doi":"10.2969/jmsj/90539053","DOIUrl":null,"url":null,"abstract":"In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible values of integer group determinants of its any abelian subgroup. By applying the refinement of a generalized Dedekind's theorem, we determine all possible values of integer group determinants of the direct product group of the cyclic group of order 8 and the cyclic group of order 2.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"74 1-2","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Generalized Dedekind's theorem and its application to integer group determinants\",\"authors\":\"Naoya YAMAGUCHI, Yuka YAMAGUCHI\",\"doi\":\"10.2969/jmsj/90539053\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible values of integer group determinants of its any abelian subgroup. By applying the refinement of a generalized Dedekind's theorem, we determine all possible values of integer group determinants of the direct product group of the cyclic group of order 8 and the cyclic group of order 2.\",\"PeriodicalId\":49988,\"journal\":{\"name\":\"Journal of the Mathematical Society of Japan\",\"volume\":\"74 1-2\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Mathematical Society of Japan\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2969/jmsj/90539053\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Mathematical Society of Japan","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2969/jmsj/90539053","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 11

摘要

本文给出了广义Dedekind定理的一个改进。此外，我们证明了任意群的整群行列式的所有可能值也是其任意阿贝尔子群的整群行列式的所有可能值。通过对广义Dedekind定理的改进，我们确定了8阶循环群与2阶循环群的直积群的整群行列式的所有可能值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Generalized Dedekind's theorem and its application to integer group determinants

In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible values of integer group determinants of its any abelian subgroup. By applying the refinement of a generalized Dedekind's theorem, we determine all possible values of integer group determinants of the direct product group of the cyclic group of order 8 and the cyclic group of order 2.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of the Mathematical Society of Japan 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Mathematical Society of Japan (JMSJ) was founded in 1948 and is published quarterly by the Mathematical Society of Japan (MSJ). It covers a wide range of pure mathematics. To maintain high standards, research articles in the journal are selected by the editorial board with the aid of distinguished international referees. Electronic access to the articles is offered through Project Euclid and J-STAGE. We provide free access to back issues three years after publication (available also at Online Index).