Topics in algebra, 2nd edition (1975) (wiley international editions)
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Topics in algebra, 2nd edition (1975) (wiley international editions)
ICDI. N. HersteinTopics. , tn,AlgebraWILEY ịSecond Editionwww.pdfgrip.comi. n. her steinUniversity of ChicagoTOPICS IN ALGEBRA2ndeditionJOHN WILEY & S Topics in algebra, 2nd edition (1975) (wiley international editions) SONS•New York • Chichester • Brisbane • Toronto • Singaporewww.pdfgrip.comTo MarianneCopyright © 1975, 1964 by Xerox Corporation.All rights reserved.Reproduction or translation of any part of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the p Topics in algebra, 2nd edition (1975) (wiley international editions) ermission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department. John WTopics in algebra, 2nd edition (1975) (wiley international editions)
iley & Sons. Inc.Library of Congress Catalog Card Number: 74-82577 Printed in the United States of America.www.pdfgrip.comPreface to the Second EditioICDI. N. HersteinTopics. , tn,AlgebraWILEY ịSecond Editionwww.pdfgrip.comi. n. her steinUniversity of ChicagoTOPICS IN ALGEBRA2ndeditionJOHN WILEY & S Topics in algebra, 2nd edition (1975) (wiley international editions) o tamper with it. However, there were certain changes I felt should be made, changes which would not affect the general style or content, but which would make the book a little more complete. I hope that I have achieved this objective in the present version.For the most part, the major changes take Topics in algebra, 2nd edition (1975) (wiley international editions) place in the chapter on group theory. When the first edition was written it was fairly uncommon for a student learning abstract algebra to have had anTopics in algebra, 2nd edition (1975) (wiley international editions)
y previous exposure to linear algebra. Nowadays quite the opposite is true; many students, perhaps even a majority, have learned something about 2x2 mICDI. N. HersteinTopics. , tn,AlgebraWILEY ịSecond Editionwww.pdfgrip.comi. n. her steinUniversity of ChicagoTOPICS IN ALGEBRA2ndeditionJOHN WILEY & S Topics in algebra, 2nd edition (1975) (wiley international editions) algebra, are indicated with a #.In the chapter on groups I have largely expanded one section, that on Sylow’s theorem, and added two others, one on direct products and one on the structure of finite abelian groups.In the previous treatment of Sylow’s theorem, only the existence of a Sylow subgroup w Topics in algebra, 2nd edition (1975) (wiley international editions) as shown. This was done following the proof of Wielandt. The conjugacy of the Sylow subgroups and their number were develODed in a series of exercisesTopics in algebra, 2nd edition (1975) (wiley international editions)
, hilt nnt in the text nrnnerwww.pdfgrip.comiv Preface to the Second EditionIn addition to the proof previously given for the existence, two other proICDI. N. HersteinTopics. , tn,AlgebraWILEY ịSecond Editionwww.pdfgrip.comi. n. her steinUniversity of ChicagoTOPICS IN ALGEBRA2ndeditionJOHN WILEY & S Topics in algebra, 2nd edition (1975) (wiley international editions) m is important, that each proof illustrates a different aspect of group theory and, above all, that I love Sylow’s theorem. The proof of the conjugacy and number of Sylow subgroups exploits double cosets. A by-product of this development is that a means is given for finding Sylow subgroups in a larg Topics in algebra, 2nd edition (1975) (wiley international editions) e set of symmetric groups.For some mysterious reason known only to myself, I had omitted direct products in the first edition. Why is beyond me. The mTopics in algebra, 2nd edition (1975) (wiley international editions)
aterial is easy, straightforward, and important. This lacuna is now filled in the section treating direct products. With this in hand, I go on in the ICDI. N. HersteinTopics. , tn,AlgebraWILEY ịSecond Editionwww.pdfgrip.comi. n. her steinUniversity of ChicagoTOPICS IN ALGEBRA2ndeditionJOHN WILEY & S Topics in algebra, 2nd edition (1975) (wiley international editions) associated with this decomposition. In point of fact, this decomposition was already in the first edition, at the end of the chapter on vector spaces, as a consequence of the structure of finitely generated modules over Euclidean rings. However, the case of a finite group is of great importance by Topics in algebra, 2nd edition (1975) (wiley international editions) itself; the section on finite abelian groups underlines this importance. Its presence in the chapter on groups, an early chapter, makes it more likelyTopics in algebra, 2nd edition (1975) (wiley international editions)
that it will be taught.One other entire section has been added at the end of the chapter on field theory. I felt that the student should see an expliICDI. N. HersteinTopics. , tn,AlgebraWILEY ịSecond Editionwww.pdfgrip.comi. n. her steinUniversity of ChicagoTOPICS IN ALGEBRA2ndeditionJOHN WILEY & S Topics in algebra, 2nd edition (1975) (wiley international editions) . In order to do so, a theorem is first proved which gives a criterion that an irreducible polynomial of degree p, p a prime, over the rational field have Sp as its Galois group. As an application of this criterion, an irreducible polynomial of degree 5 is given, over the rational field, whose Galoi Topics in algebra, 2nd edition (1975) (wiley international editions) s group is the symmetric group of degree 5.There are several other additions. More than 150 new problems arc to be found here. They are of varying degTopics in algebra, 2nd edition (1975) (wiley international editions)
rees of difficulty. Many are routine and computational, many are very difficult. Furthermore, some interpolator remarks are made about problems that hICDI. N. HersteinTopics. , tn,AlgebraWILEY ịSecond Editionwww.pdfgrip.comi. n. her steinUniversity of ChicagoTOPICS IN ALGEBRA2ndeditionJOHN WILEY & S Topics in algebra, 2nd edition (1975) (wiley international editions) scure or too terse.ICDI. N. HersteinTopics. , tn,AlgebraWILEY ịSecond Editionwww.pdfgrip.comi. n. her steinUniversity of ChicagoTOPICS IN ALGEBRA2ndeditionJOHN WILEY & SGọi ngay
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