文档介绍：Algebra
This is a volume in
PURE AND APPLIED MATHEMATICS
A Series of Monographs and Textbooks
Editors: SAMUELEILENBERG AND HYMAN BASS
A list of recent titles in this series appears at the end of this volume.
Algebra
Larry C. Grove
Department of Mathematics
The University of Arizona
Tucson, Arizona
@ 1983
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(Pure and applicd inatlieiliatic\ : )
Include.; index.
I. Algebra. Ahrtract. I. 'l'illc. II. Scric\: Pure
and applied inatlicinatics ( Acadciiiic Prcsh) :
\OAl611 510% [SlZl X3 7145
ISBN 0. I2 304620k3
PRINTED IN THE UNITED STATES OF AMERICA
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I Contents
vii
ix
xiii
Chapter I Groups
1. Groups, Subgroups, and Homomorphisms 1
2. Permutation Groups 12
3. The Symmetric and Alternating Groups 16
4. The Sylow Theorems 19
5. Solvable Groups, Normal and Subnormal Series 22
6. Products 27
7. Nilpotent Groups 29
8. Finite Abelian Groups 32
9. Free Groups 33
10. Generators and Relations 37
I 1. Some Finite Groups Classified 40
12. Further Exercises 41
Chapter I1 Rings
I. Preliminaries: Ideals and Homomorphisms 41
2. The Field of Fractions of an Integral Domain 52
3. Polynomials 54
4. Polynomials in Several Indeterminates 58
5. Divisibility and Factorization 61
6. The Chinese Remainder Theorem 7