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William Burnside was one of the three most important algebraists who were involved in the transformation of group theory from its nineteenth-century origins to a deep twentieth-century subject.Building on work of earlier mathematicians, they were able to develop sophisticated tools for solving difficult problems. All of Burnside's papers are reproduced here, organized chronologically and with a detailed bibliography.Walter Feit has contributed a foreword, and a collection of introductory essays are included to provide a commentary on Burnside's work and set it in perspective along with a modern biography that draws on archive material. ... Read more

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Originally published in 1897.This volume from the Cornell University Library's print collections was scanned on an APT BookScan and converted to JPG 2000 format by Kirtas Technologies.All titles scanned cover to cover and pages may include marks notations and other marginalia present in the original volume. ... Read more

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V 11 K FACE. "We have endeavoured in the present work to combine some of the modern developments of Higher Algebra with the subjects usually included in works on the Theory of Equations. The first ten Chapters contain all the propositions ordinarily found in elementary treatises on the subject. In these Chapters Ave have not hesitated to employ the more modern notation wherever it appeared that greater simplicity or comprehensiveness could he thereby obtained. Regarding the algebraical and the numerical solution of equations as essentially distinct problems, we have purposely omitted in Chap. "VI. numerical examples in illustration of the modes of solution there given of the cubio and biquadratic equations. Such examples do not render clearer the conception of an algebraical solution ; and, for practical purposes, the algebraical formula may be regarded as almost useless in the case of equations of a degree higher than the second. In the treatment of Elimination and Linear Transfo

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Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the difficult to read text. Read books online for free at www.forgottenbooks.org ... Read more

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This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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This volume is produced from digital images from the Cornell University Library Historical Mathematics Monographs collection. ... Read more

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Originally published in 1899.This volume from the Cornell University Library's print collections was scanned on an APT BookScan and converted to JPG 2000 format by Kirtas Technologies.All titles scanned cover to cover and pages may include marks notations and other marginalia present in the original volume. ... Read more

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Publisher: London, Scott, Greenwood ... Read more

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This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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This volume is produced from digital images created through the University of Michigan University Library's large-scale digitization efforts. The Library seeks to preserve the intellectual content of items in a manner that facilitates and promotes a variety of uses. The digital reformatting process results in an electronic version of the original text that can be both accessed online and used to create new print copies. The Library also understands and values the usefulness of print and makes reprints available to the public whenever possible. This book and hundreds of thousands of others can be found in the HathiTrust, an archive of the digitized collections of many great research libraries. For access to the University of Michigan Library's digital collections, please see http://www.lib.umich.edu and for information about the HathiTrust, please visit http://www.hathitrust.org ... Read more

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Originally published in 1909-1916.This volume from the Cornell University Library's print collections was scanned on an APT BookScan and converted to JPG 2000 format by Kirtas Technologies.All titles scanned cover to cover and pages may include marks notations and other marginalia present in the original volume. ... Read more

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PREFACE. THE theory of groups of finite order may be said to date from the time of Cauehy. To him are due the first attempts at classification with a view to forming a theory from a number of isolated facts. Galois introduced into the theory the exceedingly important idea of a self-conjugate sub-group, and the corresponding division of groups into simple and composite. Moreover, by shewing that to every equation of finite degree there corresponds a group of finite order on which all the properties of the equation depend, Galois indicated how far reaching the applications of the theory might be, and thereby contributed greatly, if indirectly, to its subsequent dcvelopement. Many additions were made, mainly by French mathematicians, during the middle part of the century. The first connected exposition of the theory was given in the third edition of M. Serret's " Gours d'Algebre Superieure," which was published in 1866. This was followed in 1870 by M. Jordan's "Traite des substitu

About the Publisher

Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the difficult to read text. Read books online for free at http://www.forgottenbooks.org ... Read more

Customer Reviews (2)

Good content, lacking in presentation
I purchased this book as a gift for a mathematician friend. I, myself, am no mathematician and am therefore no authority on the content of the text. My review, instead, concerns the look of the print. While I have no doubt that the content is excellent, I was less than satisfied with the typographical features. While the text was still readable, it was not reset, but has the look of a medium quality photo-copy. This is particularly unfortunate in a mathematics textbook because in some instances subscripts and superscripts become difficult to read.

One of the first books devoted to abstract group theory
The "Theory of Groups of Finite Order" by Burnside was first published in 1897 and a second edition in 1911; the Dover Phoenix edition is a reprint of the second edition. The book can be considered as a milestone in the theory of groups. In all prior books (with the exception of Weber's "Lehrbuch der Algebra"), the term group meant "permutation group". Burnside book intended to popularize the notion of an abstract group with the publication of this book.

Groups are defined in the second chapter, after an initial chapter on permutations. The third and fourth chapter discuss the basics of groups, including subgroups, normal subgroups, factor groups, commutators and the derived subgroup. The fifth chapter introduces the composition series of a group, and the sixth chapter discusses the automorphism group of a group. Abelian groups are discussed in chapter seven, and p-groups in chapter eight. The Sylow theorems are discussed in chapter nine. Later chapters are devoted to permutation groups, representations of groups by permutation groups, linear groups, representation theory, and even some infinite groups.

Burnside's book is still very readable, although some of terminology has changes since then. An attractive feature of the book is that it contains many more examples than one typically finds in more recent books on group theory. The exposition is very clear, so that even non-specialists can profit quite a bit. It is rather remarkable how much knowledge was already available one hundred years ago.

The book is not just interesting for historical reasons, but it provides much more examples than more recent books. Overall, I can highly recommend this classic masterpiece.
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