This Dover edition, first published in 1999, is an unabridged republication of the Second Edition of the work, which was originally published in 1958 by the Chelsea Publishing Company, New York, New York.
Author(s): Hans J. Zassenhaus
Series: Dover Books on Mathematics
Edition: 2
Publisher: Dover
Year: 1999
Language: English
Commentary: Same scan as https://libgen.is/book/index.php?md5=EF9907F6A3EA088E50C6ED280D2BCDD6 but binarized from JPG
City: Mineola, NY
Title
Preface
Preface to the Second Edition
Contents
I. Elements of Group Theory
§ 1. The Axioms of Group Theory
§ 2. Permutation Groups
§ 3. Investigation of Axioms
§ 4. A Remark on Congruence Relations
§ 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
Additional Exercises
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. 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 Theorems
§ 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 Representations 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
Appendix A: Further Exercises for Chap. II
Appendix B: Structure Theory and Direct Products
1. Projectivities
2. Modular and submodular lattices
3. Direct decompositions of lattices
4. Complemented lattices
Appendix C: Free Products and Groups Given by a Set of Generators and a System of Defining Relations
Appendix D: Further Exercises for Chap. III
Appendix E: Further Exercises for Chap. IV, § 5
Appendix F: Further Exercises for Chap. IV, § 1
Appendix G: A Theorem of Wielandt
Appendix H: Further Exercises for Chap. V, § 1
Frequently Used Symbols
Bibliography
Author Index
Index
