.

0 (hodnocen0 x )

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BK

2nd ed.

New York : Springer, cop. 1996

xvii,499 s.

ISBN 0-387-94461-3 (váz.)

Bibliogr. s. 479-490.

Grupy - teorie - algebra obecná - učebnice vysokoškolská

000015008

Preface to the Second Edition VII // Preface to the First Edition VIII // Notation xv // CHAPTER 1 // Fundamental Concepts of Group Theory 1 // 1.1. Binary Operations, Semigroups, and Groups // 1.2 Examples of Groups // 1.3 Subgroups and Cosets // 1.4 Homomorphisms and Quotient Groups // 1.5 Endomorphisms and Automorphisms // 1.6 Permutation Groups and Group Actions // CHAPTER 2 // Free Groups and Presentations 44 // 2.1. Free Groups 44 // 2.2. Presentations of Groups 50 // 2.3. Varieties of Groups 56 // CHAPTER 3 // Decompositions of a Group 63 // 3.1. Series and Composition Series 63 // 3.2. Some Simple Groups 71 // 3.3. Direct Decompositions 80 // CHAPTER 4 // Abelian Groups 93 // 4.1. Torsion Groups and Divisible Groups 93 // 4.2. Direct Sums of Cyclic and Quasicyclic Groups 98 // 4.3. Pure Subgroups and p-Groups 106 // 4.4. Torsion-Free Groups 114 // CHAPTER 5 // Soluble and Nilpotent Groups 121 // 5.1. Abelian and Central Series 121 // 5.2. Nilpotent Groups 129 // 5.3. Groups of Prime-Power Order 139 // 5.4. Soluble Groups 147 // CHAPTER 6 // Free Groups and Free Products 159 // 6.1. Further Properties of Free Groups 159 // 6.2. Free Products of Groups 167 // 6.3. Subgroups of Free Products 174 // 6.4. Generalized Free Products 184 // CHAPTER 7 // Finite Permutation Groups 192 // 7.1. Multiple Transitivity 192 // 7.2. Primitive Permutation Groups 197 // 7.3. Classification of Sharply k-Transitive Permutation Groups 203 // 7.4. The Mathieu Groups 208 // CHAPTER 8 // Representations of Groups 213 // 8.1. Representations and Modules 213 // 8.2. Structure of the Group Algebra 223 // 8.3. Characters 226 // 8.4. Tensor Products and Representations 235 // 8.5. Applications to Finite Groups 246 // CHAPTER 9 // Finite Soluble Groups 252 // 9.1. Hall t-Subgroups 252 // 9.2. Sylow Systems and System Normalizers 261 // 9.3. p-Soluble Groups 269 //

9.4. Supersoluble Groups 274 // 9.5. Formations 277 // CHAPTER 10 // The Transfer and Its Applications 285 // 10.1. The Transfer Homomorphism 285 // 10.2. Grün’s Theorems 292 // 10.3. Frobenius’s Criterion for p-Nilpotence 295 // 10.4. Thompson’s Criterion for p-Nilpotence 298 // 10.5. Fixed-Point-Free Automorphisms 305 // CHAPTER 11 // The Theory of Group Extensions 310 // 11.1. // 11.2. // 11.3. // Group Extensions and Covering Groups // Homology Groups and Cohomology Groups // 310 // 326 // 333 // The Gruenberg Resolution // 11.4. Group-Theoretic Interpretations of the (Co)homology Groups 341 // CHAPTER 12 // Generalizations of Nilpotent and Soluble Groups 356 // 12.1. Locally Nilpotent Groups 356 // 12.2. Some Special Types of Locally Nilpotent Groups 363 // 12.3. Engel Elements and Engel Groups 369 // 12.4. Classes of Groups Defined by General Series 376 // 12.5. Locally Soluble Groups 381 // CHAPTER 13 // Subnormal Subgroups 385 // 13.1. Joins and Intersections of Subnormal Subgroups 385 // 13.2. Permutability and Subnormality 393 // 13.3. The Minimal Condition on Subnormal Subgroups 396 // 13.4. Groups in Which Normality Is a Transitive Relation 402 // 13.5. Automorphism Towers and Complete Groups 408 // CHAPTER 14 // Finiteness Properties 416 // 14.1. Finitely Generated Groups and Finitely Presented Groups 416 // 14.2. Torsion Groups and the Burnside Problems 422 // 14.3. Locally Finite Groups 429 // 14.4. 2-Groups with the Maximal or Minimal Condition 437 // 14.5. Finiteness Properties of Conjugates and Commutators 439 // CHAPTER 15 // Infinite Soluble Groups // 15.1. Soluble Linear Groups // 15.2. Soluble Groups with Finiteness Conditions on Abelian Subgroups // 15.3. Finitely Generated Soluble Groups and the Maximal Condition on Normal Subgroups // 15.4. Finitely Generated Soluble Groups and Residual Finiteness //

15.5 Finitely Generated Soluble Groups and Their Frattini Subgroups // Bibliography 479 // Index 491