{"title":"特征 p > 2 中 p3 和 p4 级的非阿贝尔扩展","authors":"Grant Moles","doi":"10.1016/j.ffa.2024.102399","DOIUrl":null,"url":null,"abstract":"<div><p>This paper describes in terms of Artin-Schreier equations field extensions whose Galois group is isomorphic to any of the four non-cyclic groups of order <span><math><msup><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> or the ten non-Abelian groups of order <span><math><msup><mrow><mi>p</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>, <em>p</em> an odd prime, over a field of characteristic <em>p</em>.</p></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-Abelian extensions of degree p3 and p4 in characteristic p > 2\",\"authors\":\"Grant Moles\",\"doi\":\"10.1016/j.ffa.2024.102399\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper describes in terms of Artin-Schreier equations field extensions whose Galois group is isomorphic to any of the four non-cyclic groups of order <span><math><msup><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> or the ten non-Abelian groups of order <span><math><msup><mrow><mi>p</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>, <em>p</em> an odd prime, over a field of characteristic <em>p</em>.</p></div>\",\"PeriodicalId\":50446,\"journal\":{\"name\":\"Finite Fields and Their Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-03-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Finite Fields and Their Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1071579724000388\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finite Fields and Their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1071579724000388","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文用阿尔丁-施莱尔方程描述了在特征 p 的域上，其伽罗瓦群与四个阶 p3 的非循环群或十个阶 p4 的非阿贝尔群中的任意一个同构的域扩展，其中 p 是奇素数。
Non-Abelian extensions of degree p3 and p4 in characteristic p > 2
This paper describes in terms of Artin-Schreier equations field extensions whose Galois group is isomorphic to any of the four non-cyclic groups of order or the ten non-Abelian groups of order , p an odd prime, over a field of characteristic p.
期刊介绍：
Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering.
For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods.
The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.
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