A Course in the Theory of GroupsSpringer Science & Business Media, 1996 - 499 pages A Course in the Theory of Groups is a comprehensive introduction to the theory of groups - finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with other areas of algebra such as ring theory and homological algebra. This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional exercises are included. There are three main additions to the book. In the chapter on group extensions an exposition of Schreier's concrete approach via factor sets is given before the introduction of covering groups. This seems to be desirable on pedagogical grounds. Then S. Thomas's elegant proof of the automorphism tower theorem is included in the section on complete groups. Finally an elementary counterexample to the Burnside problem due to N.D. Gupta has been added in the chapter on finiteness properties. |
Table des matières
CHAPTER | 1 |
L | 15 |
Free Groups and Presentations | 44 |
CHAPTER 3 | 68 |
CHAPTER 5 | 79 |
Soluble and Nilpotent Groups | 121 |
Contents xiii | 147 |
CHAPTER 6 | 159 |
The Transfer and Its Applications | 285 |
CHAPTER 11 | 310 |
CHAPTER 12 | 356 |
CHAPTER 13 | 385 |
CHAPTER 14 | 416 |
CHAPTER 15 | 450 |
Bibliography | 479 |
| 488 | |
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Expressions et termes fréquents
abelian subgroup algebraically Aut G automorphism central series commutative conjugacy classes conjugate contains coset define denote direct product direct sum element of G epimorphism Exercise F-representation factors FG-module finite group finite index finite order follows Frat G free abelian free abelian group free group free product g in G G is finite G₁ G₂ GL(n group G group of order H₁ H₂ homomorphism implies induction irreducible isomorphic k-transitive K₁ Lemma Let F Let G Let H M₁ mapping matrix maximal subgroup minimal normal subgroup N₁ nilpotent group nontrivial p-group P₁ permutation group polycyclic group prime Proof Prove that G quasicyclic groups quotient group simple groups soluble group subgroup H subgroup of G subnormal subgroups subset Suppose that G Sylow p-subgroup Theorem torsion group transitive transversal trivial unique vector space wreath product write X₁