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Theory of Groups of Finite Order 2nd Edition
Posted on 2010-03-16
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More : William Burnside Preface to the 2nd Edition: Very considerable advances in the theory of groups of finite order have been made since the appearance of the first edition of this book. In particular the theory of groups of linear substitutions has been the subject of numerous and important investigations by several writers; and the reason given in the original preface for omitting any account of it no longer holds good. In fact it is now more true to say that for further advances in the abstract theory one must look largely to the representation of a group as a group of linear substitutions. There is accordingly in the present edition a large amount of new matter. Five Chapters, XIII to XVII, are devoted to the theory of groups of linear substitutions, including their invariants. In Chapter IV, which is also new, certain properties of abstract groups, to which no reference was made in the first edition, are dealt with; while Chapter XII develops more completely the investigation of the earlier sections of Chapter IX of the first edition. All the chapters dealing with the abstract theory, including that of the group of isomorphisms, have been brought together in the earlier part of the book; while from Chapter X onwards various special modes of representing a group are investigated. The last Chapter of the first edition has none to correspond to it in the present, but all results of importance which it contained are given in connections in which they naturally occur. With this exception there are no considerable changes in the matter of the first edition though there is some re-arrangement, and in places additions have been made. Quote: I Have Put A Lot Of Time And Hard Work On This Upload & Post
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