The aim of this book is to provide a concise treatment of some topics from group theory and representation theory for a one term course. It focuses on the non-commutative side of the field emphasizing the general linear group as the most important group and example. The book will enable graduate students from every mathematical field, as well as strong undergraduates with an interest in algebra, to solidify their knowledge of group theory. The reader should have a familiarity with groups, rings, and fields, along with a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to expose the reader to additional topics.
Groups and Representations (Graduate Texts in Mathematics)
and over one million other books are available for Amazon Kindle.
Learn more
FREE Two-Day Shipping for students on millions of items. Learn more |
| ||||||||||||||||||||||||
Book Description
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most Helpful Customer Reviews
9 of 11 people found the following review helpful:
5.0 out of 5 stars
An excellent supplement or a wonderful continuation,
By
This review is from: Groups and Representations (Graduate Texts in Mathematics) (Paperback)
I used this book as a 2nd year grad student with a little more than a year of graduate algebra. It worked very well as tool to solidifying my knowledge of group theory. i think it would also work as a great book to read while taking a first year algebra course. The idea of the book is to teach theory grounded in examples. In particular, Alperin uses the matrix groups as the main example for the entire book. The writing is very user friendly and the proofs are adequate. It covers basic group theory concepts, local structure (p-groups, Sylow, solvability), Parabolic Subgroups of Gl(n,F) and at the end goes into modules and representation theory.
Share your thoughts with other customers: Create your own review
|
|
Inside This Book
(learn more)
Browse and search another edition of this book.
Browse and search another edition of this book.
First Sentence:
In this introductory chapter, we review the elementary notions of group theory and develop many of the tools that we will use in the remaining chapters. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
having semisimple quotient, partial character table, row orthogonality, subnormal series, column orthogonality, staircase group, maximal normal subgroup, normalized section, root subgroups, first isomorphism theorem, minimal normal subgroup, irreducible characters, chief series, second cohomology group, semisimple algebra, composition series, complete flag, successive quotients, correspondence theorem, proper normal subgroup, nilpotent ideal, finite group theory, conjugacy classes, maximal subgroup, algebra with unit Key Phrases - Capitalized Phrases (CAPs): (learn more)
Rudiments of Group Theory, University of Chicago, Use Exercise New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this introductory chapter, we review the elementary notions of group theory and develop many of the tools that we will use in the remaining chapters. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
having semisimple quotient, partial character table, row orthogonality, subnormal series, column orthogonality, staircase group, maximal normal subgroup, normalized section, root subgroups, first isomorphism theorem, minimal normal subgroup, irreducible characters, chief series, second cohomology group, semisimple algebra, composition series, complete flag, successive quotients, correspondence theorem, proper normal subgroup, nilpotent ideal, finite group theory, conjugacy classes, maximal subgroup, algebra with unit Key Phrases - Capitalized Phrases (CAPs): (learn more)
Rudiments of Group Theory, University of Chicago, Use Exercise 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:
See all 100 books this book cites
97
books
cite this book:
See all 97 books citing this book
- Cyclotomic Fields (Graduate Texts in Mathematics) by S. Lang in Front Matter, 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)
- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Front Matter, and Back Matter
- The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) (v. 106) by Joseph H. Silverman in Back Matter (1), and Back Matter (2)
- A Course in the Theory of Groups (Graduate Texts in Mathematics) by Derek J.S. Robinson in Back Matter (1), and Back Matter (2)
See all 100 books this book cites
- Fourier Analysis on Number Fields (Graduate Texts in Mathematics) (v. 186) by Dinakar Ramakrishnan in Back Matter (1), Back Matter (2), and Back Matter (3)
- Geometry of Sporadic Groups: Volume 1, Petersen and Tilde Geometries (Encyclopedia of Mathematics and its Applications) (Vol 1) by A. A. Ivanov in Back Matter
- Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics) by Harold M. Edwards in Back Matter
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Back Matter
- Galois Theory (Graduate Texts in Mathematics) by Harold M. Edwards in Back Matter
See all 97 books citing this book
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Suggested Tags from Similar Products(What's this?)Be the first one to add a relevant tag (keyword that's strongly related to this product).
|
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
|
|
So You'd Like to...
|
|
