Linear Groups (Classic Reprint): With an Exposition of the Galois Field Theory - Couverture souple

Dickson, Leonard Eugene

Couverture souple

ISBN 10 : 1332021077 ISBN 13 : 9781332021079

Editeur : Forgotten Books, 2018

Synopsis

Excerpt from Linear Groups

Serret, Journ. De math, 1873, p. 301, p. 437; Algebre supérieure. Jordan, Traité des substitutions, pp. 14 — 18, pp. 156 — 161. Pellet, Comptes Rendus, vol. 70, p. 328, vol. 86, p. 1071, vol. 90, p. 1339, vol. 93, p. 1065; Bull. Soc. Math. De France, vol. 17, p. 156. Moore, Bull. Amer. Math. Soc., Dec., 1893; Congress Mathematical Papers. Dickson, Bull. Amer. Math. Soc, vol. 3, pp. 381 — 389; vol. 6, pp. 203 — 204.

A propos du livre

Présentation de l'éditeur

Excerpt from Linear Groups With an Exposition, of the Galois Field Theory

Since the appearance in 1870 of the great work of Camille Jordan on substitutions and their applications there have been many important additions to the theory of finite groups. The books of Netto, Weber and Burnside have brought up to date the theory of abstract and substitution groups. On the analytic side the theory of linear groups has received much attrition in view of their frequent occurrence in mathematical problems both of theory and of application. The theory of collineation groups will be treated in a forthcoming volume by Loewy. There remains the subject of linear groups in a finite field (including linear congruence groups) having immediate application in many problems of geometry and function-theory and furnishing a natural method for the investigation of extensive classes of important groups. The present volume is intended as an introduction to this subject. While the exposition is restricted to groups in a finite field (endliche Korper) the method of investigation is applicable to groups in an infinite field; corresponding theorems for continuous and collineation groups may often be enunciated without modification of the text.

The earlier chapters of the text are devoted to an elementary exposition of the theory of Galois Fields chiefly in their abstract form. The conception of an abstract field is introduced by means of the simplest example that of the classes of residues with respect to a prime modulus. In view of the theorem of Moore that every finite field may be represented as a Galois Field, our investigations acquire complete generality when we take as basis the general Galois Field. It was found to be impracticable to attempt to indicate the sources of the individual theorems and conceptions of the theory. Aside from the independent discovery of theorems by different writers and a general lack of reference to earlier papers, the later writers have given...

Présentation de l'éditeur

This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide. This text refers to the Bibliobazaar edition.

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1332021077
• ISBN 13: 9781332021079
• Reliure: Broché
• Nombre de pages: 326
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