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
THE ISOMORPHISM THEOREMS | 11 |
PERMUTATION GROUPS | 32 |
THE SYLOW THEOREMS | 56 |
Copyright | |
12 other sections not shown
Other editions - View all
Common terms and phrases
a₁ a₂ abelian group affine Assume automorphism B₁ B₂ commute composition series conjugacy classes conjugate Corollary cosets cyclic groups defined Definition Let denoted diagram direct product direct sum disjoint elements of G example Exercise factor set finite group follows free abelian free abelian group free group function G contains G-set G₁ G₂ group G group of order H₁ hence HINT HNN extension homomorphism implies induction infinite integer isomorphic K₁ kernel L₂ Lemma Let F Let G Let H matrix multiplicative group nilpotent nonsingular nonzero normal subgroup notation one-one correspondence p-group permutation polynomial prime Proof Let Prove that G reader semidirect product semigroup shows simple group solvable solvable group stable letter Steiner system subgroup H subgroup of G subgroup of order subset subword summand Sylow p-subgroup Theorem torsion-free transitive G-set transvection unique vector space word problem x₁