{"title":"The Theory of Equations: with an Introduction to the Theory of Binary Algebraic Forms","authors":"","doi":"10.1038/065390a0","DOIUrl":null,"url":null,"abstract":"IN this new edition of a well-known and popular treatise the principal change is the addition of a chapter on the theory of substitutions and groups. Following the methods of Serret, Jordan and Netto, the authors give just so much of the elementary theory of substitution-groups as to enable them to prove the fundamental property of the Galoisian resolvent of an equation, and to demonstrate that the general equation of any degree higher than the fourth cannot be solved by an algebraic formula. It is strange that no reference is given to the work of Kronecker and others on equations which do admit of algebraic solution. The Theory of Equations: with an Introduction to the Theory of Binary Algebraic Forms. By W. S. Burnside A. W. Panton Fourth edition. 2 vols. Pp. xiv + 286 and xii + 292. (Dublin: Hodges, Figgis and Co., Ltd.; London: Longmans, Green and Co., 1899, 1901.)","PeriodicalId":18787,"journal":{"name":"Nature","volume":"65 1687","pages":"390-390"},"PeriodicalIF":50.5000,"publicationDate":"1902-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1038/065390a0","citationCount":"65","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nature","FirstCategoryId":"103","ListUrlMain":"https://www.nature.com/articles/065390a0","RegionNum":1,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 65
Abstract
IN this new edition of a well-known and popular treatise the principal change is the addition of a chapter on the theory of substitutions and groups. Following the methods of Serret, Jordan and Netto, the authors give just so much of the elementary theory of substitution-groups as to enable them to prove the fundamental property of the Galoisian resolvent of an equation, and to demonstrate that the general equation of any degree higher than the fourth cannot be solved by an algebraic formula. It is strange that no reference is given to the work of Kronecker and others on equations which do admit of algebraic solution. The Theory of Equations: with an Introduction to the Theory of Binary Algebraic Forms. By W. S. Burnside A. W. Panton Fourth edition. 2 vols. Pp. xiv + 286 and xii + 292. (Dublin: Hodges, Figgis and Co., Ltd.; London: Longmans, Green and Co., 1899, 1901.)
在这本广受欢迎的著名论著的新版中，主要的变化是增加了一章关于置换和群的理论。作者沿用了塞雷特、乔丹和内托的方法，给出了大量关于置换群的基本理论，使他们能够证明方程的伽罗瓦解析式的基本性质，并证明任何高于四度的一般方程都无法用代数式求解。奇怪的是，书中没有提到克罗内克等人关于可以用代数式求解的方程的研究成果。方程理论：二元代数形式理论导论》。W. S. Burnside A. W. Panton 著 第四版。2 卷。第 xiv + 286 页和第 xii + 292 页。(都柏林：Hodges, Figgis and Co., Ltd.; 伦敦：Longmans, Green and Co：Longmans, Green and Co., 1899, 1901）。
期刊介绍：
Nature is a prestigious international journal that publishes peer-reviewed research in various scientific and technological fields. The selection of articles is based on criteria such as originality, importance, interdisciplinary relevance, timeliness, accessibility, elegance, and surprising conclusions. In addition to showcasing significant scientific advances, Nature delivers rapid, authoritative, insightful news, and interpretation of current and upcoming trends impacting science, scientists, and the broader public. The journal serves a dual purpose: firstly, to promptly share noteworthy scientific advances and foster discussions among scientists, and secondly, to ensure the swift dissemination of scientific results globally, emphasizing their significance for knowledge, culture, and daily life.
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