Group Extensions, Representations, and the Schur Multiplicator

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This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes

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Product Details

  • ISBN-13: 9780387119540
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 5/1/1983
  • Series: Lecture Notes in Mathematics
  • Pages: 278

Table of Contents

Introduction 1

Chapter I Group Extensions with Abelian Kernel

1 The Calculus of Induced Extensions 5

2 The Exact Sequence for Opext 19

3 The Schur Multiplicator and the Universal Coefficient Theorem 28

4 The Ganea Map of Central Extensions 40

5 Compatibility with Other Approaches 47

6 Corestriction (Transfer) 58

Chapter II Schur's Theory of Projective Representations

1 Projective Representations 67

2 The Problem of Lifting Homomorphisms 77

3 Representation Groups 91

4 Representation Groups of Free and Direct Products 101

5 The Covering Theory of Perfect Groups 113

Chapter III Isoclinism

1 Isoclinic Groups and Central Extensions 123

2 Isoclinism and the Schur Multiplicator 137

3 The Isomorphism Classes of Isoclinic Central Extensions and the Hall Formulae 144

4 On Presentations of Isoclinic Groups 155

5 Representations of Isoclinic Groups 169

Chapter IV Other Group-Theoretic Applications of the Schur Multiplicator

1 Deficiency of Finitely Presented Groups 179

2 Metacyclic Groups 193

3 The Precise Center of an Extension Group and Capable Groups 204

4 Examples of the Computation of Z*(G) 213

5 Preliminaries on Group Varieties 227

6 Central Extensions and Varieties 233

7 Schur-Baer Multiplicators and Isologism 244

Bibliography 261

Index of Special Symbols 271

Subject Index 274

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