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
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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
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Most Helpful Customer Reviews
24 of 24 people found the following review helpful:
3.0 out of 5 stars
Solid, but occasionally frustrating,
By
This review is from: An Introduction to the Theory of Groups (Hardcover)
I used this book as a means of writing my senior thesis on the clasification of the projective unimodular groups and the Mathieu groups as being simple. Most of the proofs were well constructed and easy to follow. What this books lacks is a proof reading. Several of the proofs make no sense in the form in which they are written. Also, his notation at times becomes cluttered and not easy to follow. One can imagine how difficult notation can be in general, but when it is full of typographical errors, it can be almost impossible to wade through without the help of someone who knows the material. This book is certainly not a waste of time to read and is very good as a reference for theorems concerning finite groups, however do not put all your eggs in one basket and base your education on this one book.
19 of 19 people found the following review helpful:
3.0 out of 5 stars
Good book but many errors,
By "thrustl" (North Tonawanda, NY United States) - See all my reviews
This review is from: An Introduction to the Theory of Groups (Hardcover)
This is a good book, well-organized and contains many useful materials. However I do not recommend it as an independent study textbook (which is what I did). There are many errors, most of them are typographical but some of them are wrong numbers which are very difficult to correct, especially in the exercises given. And the exercises are very important -- the following discussions and proofs depend on some of them. Springer published a "corrected second printing" in 1999 but obviously they didn't do a good job (I purchased the new one and I got the old one in the library).
13 of 13 people found the following review helpful:
5.0 out of 5 stars
Fun but not easy,
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This review is from: An Introduction to the Theory of Groups (Hardcover)
I am not sure I would take this specific book to a desert island but I would highly recommend it to anyone who is in possession of patience, self-motivation and willingness to spend time working through both the problems and any gaps that may occur within the proofs. This book can be used both by Graduate students or as a topics/independent study course for well prepared and motivated undergraduates.In general, you can be guaranteed that the exposition present within any book by Rotman is par-excellence and this book is no exception. The material is presented in a sound and definite logical manner, which results in gently directing the reader through an 'introduction' to group theory by presenting the material in well thought out and bite sized portions. The only negative aspect of this book, which is minimal as best, is the authors choice of notation, for example the notation used to define G-sets in chapter 3 does not necessarily do the topic justice since G-sets in their own right are an important concept. But, as stated, this is the only complaint and is easily remedied. Enjoy!
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Inside This Book
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First Sentence:
Generalizations of the quadratic formula for cubic and quartic polynomials were discovered in the sixteenth century, and one of the major mathematical problems thereafter was to find analogous formulas for the roots of polynomials of higher degree; all attempts failed. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
free group with basis, nonsingular semilinear transformation, solvable series, centerless group, stable letters, automorphism tower, nondegenerate space, full subcomplex, solvable word problem, displayed generators, elementary transvection, indecomposable group, principal derivation, normal endomorphism, solvable conjugacy problem, injective property, cyclic summands, nonisomorphic groups, coset enumeration, transitive extension, connected subcomplex, left transversal, basic subgroup, affine isomorphism, simplicial map Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cambridge University Press, Cohomology of Groups, Galois Theory, Homological Algebra, Academic Press, Algebraic Topology, Oxford University Press, The Isomorphism Theorems, Cycle Structure Number Order Parity, Mac Lane, Mathematical Logic, Some Simple Linear Groups, Axiom of Choice, Princeton University Press, University of Chicago Press New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Generalizations of the quadratic formula for cubic and quartic polynomials were discovered in the sixteenth century, and one of the major mathematical problems thereafter was to find analogous formulas for the roots of polynomials of higher degree; all attempts failed. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
free group with basis, nonsingular semilinear transformation, solvable series, centerless group, stable letters, automorphism tower, nondegenerate space, full subcomplex, solvable word problem, displayed generators, elementary transvection, indecomposable group, principal derivation, normal endomorphism, solvable conjugacy problem, injective property, cyclic summands, nonisomorphic groups, coset enumeration, transitive extension, connected subcomplex, left transversal, basic subgroup, affine isomorphism, simplicial map Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cambridge University Press, Cohomology of Groups, Galois Theory, Homological Algebra, Academic Press, Algebraic Topology, Oxford University Press, The Isomorphism Theorems, Cycle Structure Number Order Parity, Mac Lane, Mathematical Logic, Some Simple Linear Groups, Axiom of Choice, Princeton University Press, University of Chicago Press New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
cite this book:
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- An Introduction to Algebraic Topology (Graduate Texts in Mathematics) by Joseph J. Rotman on page 497, Back Matter (1), and Back Matter (2)
- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang in Back Matter (1), Back Matter (2), and Back Matter (3)
- Homological Algebra (PMS-19) by Henri Cartan on page 473, and page 495
- Abelian Groups (Lecture Notes in Pure and Applied Mathematics) by Laszlo Fuchs on page 473, and page 496
- Group Theory (Dover Books on Mathematics) by W. R. Scott on page 473, and page 497
See all 100 books this book cites
- Fuzzy Group Theory (Studies in Fuzziness and Soft Computing) by John N. Mordeson on page 89, and page 200
- Introduction to Lie Algebras (Springer Undergraduate Mathematics Series) by K. Erdmann in Back Matter (1), and Back Matter (2)
- An Introduction to Algebraic Topology (Graduate Texts in Mathematics) by Joseph J. Rotman in Back Matter (1), and Back Matter (2)
- 1,001 Low-Fat Vegetarian Recipes: Delicious, Easy-to-Make, Healthy Meals for Everyone by Sue Spitler on page 197
- Galois Theory (Graduate Texts in Mathematics) by Harold M. Edwards in Back Matter
See all 100 books citing this book
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