An Introduction to the Theory of GroupsSpringer Science & Business Media, 6 déc. 2012 - 517 pages 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 |
Table des matières
| 1 | |
The Isomorphism Theorems | 20 |
Symmetric Groups and GSets | 43 |
29 | 52 |
40 | 58 |
CHAPTER 4 | 73 |
28 | 85 |
Normal Series | 89 |
Affine Geometry | 264 |
Sharply 3Transitive Groups | 281 |
CHAPTER 10 | 307 |
Divisible and Reduced Groups | 320 |
Character Groups | 335 |
Semigroup Interlude | 349 |
Fundamental Groups of Complexes | 366 |
The NielsenSchreier Theorem | 383 |
Solvable Groups | 102 |
46 | 118 |
The Fundamental Theorem of Finite Abelian Groups | 131 |
CHAPTER 8 | 133 |
CHAPTER 7 | 154 |
Semidirect Products | 167 |
Theorems of SchurZassenhaus and Gaschütz | 188 |
Some Simple Linear Groups | 217 |
Classical Groups | 234 |
CHAPTER 9 | 247 |
Amalgams | 401 |
CHAPTER 12 | 418 |
Cancellation Diagrams | 433 |
The Higman Imbedding Theorem | 450 |
Some Applications | 464 |
APPENDIX II | 477 |
Bibliography | 495 |
| 507 | |
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Expressions et termes fréquents
a₁ abelian group affine Algebra assume Aut(K automorphism B₁ bijection central extension commute complex conjugate contains Corollary cosets cyclic groups defined Definition denoted diagram direct sum disjoint divisor example Exercise extension with base factor set field finite group finitely presented group fixes follows free abelian free abelian group free group function G-set G₁ gives GL(V group G group of order H₁ hence Hint HNN extension homomorphism imbedded induction infinite injection integer isomorphism K₁ Lemma Let G linear matrix maximal multiplication nilpotent nonzero normal subgroup notation p-group permutation polynomial prime Proof Prove relations semidirect product semigroup shows simple groups simplex stable letters Steiner system subcomplex subgroup H subgroup of G subgroup of order subset subword summand surjective Sylow p-subgroup Theorem torsion-free transitive G-set transvection transversal unique vector space wreath product y₁ Z₂