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Index
Cover Title Page Copyright Page Preface Preface to The Second Edition I. Elements of Group Theory
§ 1. The Axioms of Group Theory § 2. Permutation Groups § 3. Investigation of Axioms § 4. Subgroups § 5. Cyclic Groups § 6. Finite Rotation Groups § 7. Calculus of Complexes § 8. The Concept of Normal Subgroup § 9. Normalizer, Class Equation § 10. A Theorem of Frobenius
II. The Concept of Homomorphy and Groups with Operators
§ 1. Homomorphisms § 2. Representation of Groups by Means of Permutations § 3. Operators and Operator Homomorphies § 4. On the Automorphisms of a Group § 5. Normal Chains and Normal Series § 6. Commutator Groups and Commutator Forms § 7. On the Groups of an Algebra
III. The Structure and Construction of Composite Groups
§ 1. Direct Products § 2. Theorems on Direct Products § 3. Abelian Groups § 4. Basis Theorem for Abelian Groups § 5. On the Order Ideal § 6. Extension Theory § 7. Extensions with Cyclic Factor Group § 8. Extensions with Abelian Factor Group § 9. Splitting Groups
IV. Sylow p-Groups and p-Groups
§ 1. The Sylow Theorem § 2. Theorems on Sylow p-Groups § 3. On p-Groups § 4. On the Enumeration Theorems of the Theory of p-Groups § 5. On the Descending Central Series § 6. Hamiltonian Groups § 7. Applications of Extension Theory
V. Transfers into A Subgroup
§ 1. Monomial Representation and Transfers into a Subgroup § 2. The Theorems of Burnside and Grün § 3. Groups whose Sylow Groups are All Cyclic § 4. The Principal Ideal Theorem
Appendixes
A. Further Exercises for Chap. II B. Structure Theory and Direct Products. A Treatment of Chap. III, § 2 on the Lattice-Theoretical Level C. Free Products and Groups Given by a Set of Generators and a System of Defining Relations D. Further Exercises for Chap. III E. Further Exercises for Chap. IV, § 5 F. Further Exercises for Chap. IV., § 1 G. A Theorem of Wielandt. An Addendum to Chap. IV H. Further Exercises for Chap. V, § 1
Frequently used Symbols Bibliography Author Index Index
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