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

Dickson, Leonard Eugene

9781332021079: Linear Groups (Classic Reprint): With an Exposition of the Galois Field Theory: With an Exposition of the Galois Field Theory (Classic Reprint)

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ISBN 10: 1332021077 ISBN 13: 9781332021079

Verlag: Forgotten Books, 2018

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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.

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

Serret, Journ. De math, 1873, p. 301, p. 437; Algebre sup�rieure.

Jordan, Trait� 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.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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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 wide generalizations of the results of earlier investigators. It will suffice to give the following list of references on Galois Fields and higher irreducible congruences:

Galois, "Sur la th�orie des nombres", Bulletin des sciences math�matiques de M. F�russac, 1830; Journ. de math�matiques, 1846.

Schonemann, Crelle, vol. 31 (1846), pp. 269 - 325.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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