An Introduction to the Theory of GroupsAnyone 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 |
Contents
CHAPTER | 1 |
CHAPTER 2 | 20 |
Symmetric Groups and GSets | 43 |
222222358 | 52 |
Counting Orbits | 58 |
CHAPTER 4 | 73 |
Normal Series | 89 |
Solvable Groups | 102 |
Classical Groups | 234 |
CHAPTER 9 | 247 |
Affine Geometry | 264 |
Sharply 3Transitive Groups | 281 |
CHAPTER 10 | 307 |
Divisible and Reduced Groups | 320 |
Character Groups | 335 |
The Higman Imbedding Theorem | 433 |
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Common terms and phrases
a e G a₁ abelian group Algebra assume Aut(G Aut(K automorphism B₁ basis bijection central extension commute conjugacy classes conjugate contains Corollary cyclic groups defined Definition denoted direct product direct sum disjoint divisor elements of G example Exercise factor set field finite group finitely presented fixes follows free abelian 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 matrix multiplication nilpotent nonempty nonzero normal subgroup notation p-group permutation polynomial prime Proof Prove right cosets semidirect product semigroup shows simple groups solvable stable letters Steiner system subgroup H subgroup of G subgroup of order subset summands surjective Sylow p-subgroup Theorem torsion-free transpositions transversal unique v₁ vector space wreath product y₁ Z₂