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An Introduction to the Theory of Groups Graduate Texts in Mathematics, VG 1976

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US $57.77
ApproximatelyRM 242.93
Condition:
Very Good
“Springer, 4th Ed. Vintage. Hardcover. From the personal collection of a former Computer, Engineering ”... Read moreabout condition
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Item specifics

Condition
Very Good
A book that has been read but is in excellent condition. No obvious damage to the cover, with the dust jacket included for hard covers. No missing or damaged pages, no creases or tears, and no underlining/highlighting of text or writing in the margins. May be very minimal identifying marks on the inside cover. Very minimal wear and tear. See all condition definitionsopens in a new window or tab
Seller Notes
“Springer, 4th Ed. Vintage. Hardcover. From the personal collection of a former Computer, ...
Book Title
An Introduction to the Theory of Groups (Graduate Texts in Mathem
Country/Region of Manufacture
United States
Signed
No
Personalized
No
Vintage
Yes
Book Series
Graduate Texts in Mathematics
Genre
vintage math textbook, graduate group theory, advanced algebra in
Ex Libris
No
Original Language
English
Era
1990s, 20th Century
Edition
4th edition
Inscribed
No
Signed By
NA
Personalize
No
Intended Audience
Adults
Narrative Type
Nonfiction
Literary Movement
STEM education literature, group theory academic tradition, rigor
Topic
Joseph J. Rotman, group theory textbook, abstract algebra advance
ISBN
9780387942858

About this product

Product Identifiers

Publisher
Springer New York
ISBN-10
0387942858
ISBN-13
9780387942858
eBay Product ID (ePID)
697274

Product Key Features

Number of Pages
Xv, 517 Pages
Language
English
Publication Name
Introduction to the Theory of Groups
Subject
Group Theory, Algebra / Abstract
Publication Year
1994
Features
Revised
Type
Textbook
Author
Joseph J. Rotman
Subject Area
Mathematics
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover

Dimensions

Item Height
0.5 in
Item Weight
72.3 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Edition Number
4
Intended Audience
Scholarly & Professional
LCCN
94-006507
TitleLeading
An
Dewey Edition
19
Reviews
Fourth Edition J.J. Rotman An Introduction to the Theory of Groups "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route."-MATHEMATICAL REVIEWS, Fourth Edition J.J. Rotman An Introduction to the Theory of Groups "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route."--MATHEMATICAL REVIEWS, Fourth EditionJ.J. RotmanAn Introduction to the Theory of Groups"Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route."-MATHEMATICAL REVIEWS
Series Volume Number
148
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
512/.22
Edition Description
Revised edition
Table Of Content
1 Groups and Homomorphisms.- Permutations.- Cycles.- Factorization into Disjoint Cycles.- Even and Odd Permutations.- Semigroups.- Groups.- Homomorphisms.- 2 The Isomorphism Theorems.- Subgroups.- Lagrange's Theorem.- Cyclic Groups.- Normal Subgroups.- Quotient Groups.- The Isomorphism Theorems.- Correspondence Theorem.- Direct Products.- 3 Symmetric Groups and G-Sets.- Conjugates.- Symmetric Groups.- The Simplicity of An.- Some Representation Theorems.- G-Sets.- Counting Orbits.- Some Geometry.- 4 The Sylow Theorems.- p-Groups.- The Sylow Theorems.- Groups of Small Order.- 5 Normal Series.- Some Galois Theory.- The Jordan-Hölder Theorem.- Solvable Groups.- Two Theorems of P. Hall.- Central Series and Nilpotent Groups.- p-Groups.- 6 Finite Direct Products.- The Basis Theorem.- The Fundamental Theorem of Finite Abelian Groups.- Canonical Forms; Existence.- Canonical Forms; Uniqueness.- The Krull--Schmidt Theorem.- Operator Groups.- 7 Extensions and Cohomology.- The Extension Problem.- Automorphism Groups.- Semidirect Products.- Wreath Products.- Factor Sets.- Theorems of Schur-Zassenhaus and Gaschütz.- Transfer and Burnside's Theorem.- Projective Representations and the Schur Multiplier.- Derivations.- 8 Some Simple Linear Groups.- Finite Fields.- The General Linear Group.- PSL(2, K).- PSL(m, K).- Classical Groups.- 9 Permutations and the Mathieu Groups.- Multiple Transitivity.- Primitive G-Sets.- Simplicity Criteria.- Affine Geometry.- Projective Geometry.- Sharply 3-Transitivc Groups.- Mathieu Groups.- Steiner Systems.- 10 Abelian Groups.- Basics.- Free Abelian Groups.- Finitely Generated Abelian Groups.- Divisible and Reduced Groups.- Torsion Groups.- Subgroups of ?.- Character Groups.- 11 Free Groups and Free Products.- Generators and Relations.- SemigroupInterlude.- Coset Enumeration.- Presentations and the Schur Multiplier.- Fundamental Groups of Complexes.- Tietze's Theorem.- Covering Complexes.- The Nielscn-Schreier Theorem.- Free Products.- The Kurosh Theorem.- The van Kampen Theorem.- Amalgams.- HNN Extensions.- 12 The Word Problem.- Turing Machines.- The Markov--Post Theorem.- The Novikov--Boone--Britton Theorem: Sufficiency of Boone's Lemma.- Cancellation Diagrams.- The Novikov--Boone--Britton Theorem: Necessity of Boone's Lemma.- The Higman Imbedding Theorem.- Some Applications.- Epilogue.- Appendix I Some Major Algebraic Systems.- Appendix II Equivalence Relations and Equivalence Classes.- Appendix III Functions.- APPENDIX IV Zorn's Lemma.- APPENDIX V Countability.- APPENDIX VI Commutative Rings.- Notation.
Synopsis
Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions. From the reviews: "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route." --MATHEMATICAL REVIEWS, Anyone who has studied "abstract algebra" and linear algebra as an undergraduate can understand this book. This edition has been completely revised and reorganized, without however losing any of the clarity of presentation that was the hallmark of the previous editions. The first six chapters provide ample material for a first course: beginning with the basic properties of groups and homomorphisms, topics covered include Lagrange's theorem, the Noether isomorphism theorems, symmetric groups, G -sets, the Sylow theorems, finite Abelian groups, the Krull-Schmidt theorem, solvable and nilpotent groups, and the Jordan-Holder theorem. The middle portion of the book uses the Jordan-Holder theorem to organize the discussion of extensions (automorphism groups, semidirect products, the Schur-Zassenhaus lemma, Schur multipliers) and simple groups (simplicity of projective unimodular groups and, after a return to G -sets, a construction of the sporadic Mathieu groups).
LC Classification Number
QA174-183

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