An Introduction to the Theory of Groups

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Springer Science & Business Media, 13 août 1999 - 517 pages
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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.

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"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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Table des matières

CHAPTER
1
Factorization into Disjoint Cycles
6
CHAPTER 2
20
Symmetric Groups and GSets
43
CHAPTER 4
73
Normal Series
89
Solvable Groups
102
pGroups
119
CHAPTER 10
307
CHAPTER 11
343
Semigroup Interlude
349
Presentations and the Schur Multiplier
358
Fundamental Groups of Complexes
366
Tietzes Theorem
374
The NielsenSchreier Theorem
383
The Kurosh Theorem
391

Canonical Forms Existence
133
Operator Groups
151
CHAPTER 12
154
Semidirect Products
167
Theorems of SchurZassenhaus and Gaschütz
188
Projective Representations and the Schur Multiplier
201
Some Simple Linear Groups
217
CHAPTER 9
246
Amalgams
401
HNN Extensions
407
The Word Problem
418
Cancellation Diagrams
425
Epilogue
471
APPENDIX II
477
Commutative Rings
485
Droits d'auteur

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