论四元数、二面括号和霍普夫-伽罗瓦结构

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2024-11-19 DOI:10.1016/j.jalgebra.2024.11.011

Nigel P. Byott , Fabio Ferri

{"title":"论四元数、二面括号和霍普夫-伽罗瓦结构","authors":"Nigel P. Byott , Fabio Ferri","doi":"10.1016/j.jalgebra.2024.11.011","DOIUrl":null,"url":null,"abstract":"<div><div>We prove a conjecture of Guarnieri and Vendramin on the number of braces of a given order whose multiplicative group is a generalised quaternion group. At the same time, we give a similar result where the multiplicative group is dihedral. We also enumerate Hopf-Galois structures of abelian type on Galois extensions with generalised quaternion or dihedral Galois group.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 72-102"},"PeriodicalIF":0.8000,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the number of quaternion and dihedral braces and Hopf–Galois structures\",\"authors\":\"Nigel P. Byott , Fabio Ferri\",\"doi\":\"10.1016/j.jalgebra.2024.11.011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We prove a conjecture of Guarnieri and Vendramin on the number of braces of a given order whose multiplicative group is a generalised quaternion group. At the same time, we give a similar result where the multiplicative group is dihedral. We also enumerate Hopf-Galois structures of abelian type on Galois extensions with generalised quaternion or dihedral Galois group.</div></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":\"665 \",\"pages\":\"Pages 72-102\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869324006185\",\"RegionNum\":2,\"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 Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324006185","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了瓜尔尼里和文德拉明关于乘法群为广义四元数的给定阶的括号数的猜想。同时，我们还给出了乘法群为二面体群时的类似结果。我们还列举了具有广义四元组或二面体伽罗瓦群的伽罗瓦扩展上的无边型霍普夫-伽罗瓦结构。

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

On the number of quaternion and dihedral braces and Hopf–Galois structures

We prove a conjecture of Guarnieri and Vendramin on the number of braces of a given order whose multiplicative group is a generalised quaternion group. At the same time, we give a similar result where the multiplicative group is dihedral. We also enumerate Hopf-Galois structures of abelian type on Galois extensions with generalised quaternion or dihedral Galois group.

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 Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.