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A Course in the Theory of Groups (Graduate Texts in Mathematics, nr. 80)

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en Limba Engleză Paperback – 08 Sep 2012
A Course in the Theory of Groups is a comprehensive introduction to the theory of groups - finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with other areas of algebra such as ring theory and homological algebra.
This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional exercises are included. There are three main additions to the book. In the chapter on group extensions an exposition of Schreier's concrete approach via factor sets is given before the introduction of covering groups. This seems to be desirable on pedagogical grounds. Then S. Thomas's elegant proof of the automorphism tower theorem is included in the section on complete groups. Finally an elementary counterexample to the Burnside problem due to N.D. Gupta has been added in the chapter on finiteness properties.
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  Springer – 08 Sep 2012 24980 lei  7-9 săpt. +27141 lei  12-20 zile
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Specificații

ISBN-13: 9781461264439
ISBN-10: 146126443X
Pagini: 524
Ilustrații: XVII, 502 p.
Dimensiuni: 155 x 235 x 30 mm
Greutate: 0.8 kg
Ediția: 2nd ed. 1996. Softcover reprint of the original 2nd ed. 1996
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics

Locul publicării: New York, NY, United States

Public țintă

Graduate

Cuprins

1 Fundamental Concepts of Group Theory.- 2 Free Groups and Presentations.- 3 Decompositions of a Group.- 4 Abelian Groups.- 5 Soluble and Nilpotent Groups.- 6 Free Groups and Free Products.- 7 Finite Permutation Groups.- 8 Representations of Groups.- 9 Finite Soluble Groups.- 10 The Transfer and Its Applications.- 11 The Theory of Group Extensions.- 12 Generalizations of Nilpotent and Soluble Groups.- 13 Subnormal Subgroups.- 14 Finiteness Properties.- 15 Infinite Soluble Groups.

Recenzii

Second Edition
D.J.S. Robinson
A Course in the Theory of Groups
"This book is an excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The fifteen chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties . . . This book is highly recommended."—ACTA SCIENTIARUM MATHEMATICARUM