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Linear Groups (Classic Reprint): With an Exposition of the Galois Field Theory: With an Exposition of the Galois Field Theory (Classic Reprint) - Tapa blanda
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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 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
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 théorie des nombres", Bulletin des sciences mathématiques de M. Férussac, 1830; Journ. de mathématiques, 1846.
Schonemann, Crelle, vol. 31 (1846), pp. 269 - 325.
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- Año de publicación2018
- ISBN 10 1332021077
- ISBN 13 9781332021079
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- IdiomaInglés
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Linear Groups: With an Exposition of the Galois Field Theory (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book presents a comprehensive examination of linear groups in a Galois Field. It is an essential resource for those interested in the field of finite groups, specifically the theories of abstract and substitution groups. Galois Fields, also known as finite fields, are algebraic structures with a finite number of elements. Since their introduction in the 19th century, Galois Fields have received considerable attention in various branches of mathematics. The book provides a detailed study of the structure, properties, and applications of linear groups within Galois Fields. It presents foundational concepts and delves into advanced topics, including the classification of linear homogeneous groups and the study of subgroups and their properties. The book's insights have significant implications for understanding the behavior and applications of linear groups in Galois Fields, making it an invaluable resource for mathematicians, computer scientists, and anyone interested in the interplay between algebra and finite group theory. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781332021079_0
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