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Course in Group Theory

ISBN-10: 0198534590
ISBN-13: 9780198534594
Edition: 1996
List price: $66.00 Buy it from $41.95
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Description: This book is an excellent and self-contained introduction to the theory of groups, covering all topics likely to be encountered in undergraduate courses. It aims to stimulate and encourage undergraduates to find out more about their subject. The  More...

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Book details

List price: $66.00
Copyright year: 1996
Publisher: Oxford University Press, Incorporated
Publication date: 7/11/1996
Binding: Paperback
Pages: 304
Size: 6.25" wide x 9.50" long x 0.75" tall
Weight: 0.528
Language: English

This book is an excellent and self-contained introduction to the theory of groups, covering all topics likely to be encountered in undergraduate courses. It aims to stimulate and encourage undergraduates to find out more about their subject. The book takes as its theme the various fundamental classification theorems in finite group theory, and the text is further explained in numerous examples and exercises, and summaries at the end of each chapter.

Definitions and examples
Maps and relations on sets
Elementary consequences of the definitions
Subgroups
Cosets and Lagrange's Theorem
Error-correcting codes
Normal subgroups and quotient groups
The Homomorphism Theorem
Permutations
The Orbit-Stabilizer Theorem
The Sylow Theorems
Applications of Sylow Theorems
Direct products
The classification of finite abelian groups
The Jordan-Holder Theorem
Composition factors and chief factors
Soluble groups
Examples of soluble groups
Semi-direct products and wreath products
Extensions
Central and cyclic extensions
Groups with at most 31 elements
The projective special linear groups
The Mathieu groups
The classification of finite simple groups
Prerequisites from Number Theory and Linear Algebra
Groups of order [ 32
Solutions to Exercises
Bibliography
Index

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