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
City: Mineola, NY
Preface to First Edition . v
Preface to Second Edition. vii
I. Elements of group theory
§ 1. The Axioms of Group Theory . 1
§ 2. Permutation Groups . 4
§ 3. Investigation of Axioms . 9
§ 4. Subgroups . 10
§ 5. Cyclic Groups . 15
§ 6. Finite Rotation Groups . 16
§ 7. Calculus of Complexes. 19
§ 8. The Concept of Normal Subgroup. 23
§ 9. Normalizes Class Equation . 24
§ 10. A Theorem of Frobenius . 27
II. The concept of homomorphy and
GROUPS WITH OPERATORS
§ 1. Homomorphisms . 35
§ 2. Representation of Groups by Means of Permutations. 39
§ 3. Operators and Operator Homomorphies. 44
§ 4. On the Automorphisms of a Group. 47
§ 5. Normal Chains and Normal Series. 57
§ 6. Commutator Groups and Commutator Forms. 78
§ 7. On the Groups of an Algebra. 84
III. The structure and construction of
COMPOSITE GROUPS
§ 1. Direct Products .109
§ 2. Theorems on Direct Products.112
§3. Abelian Groups .117
§ 4. Basis Theorem for Abelian Groups.121
§ 5. On the Order Ideal.123
§ 6. Extension Theory .124
§ 7. Extensions with Cyclic Factor Group.128
§ 8. Extensions with Abelian Factor Group .130
§ 9. Splitting Groups .133
IV. SYLOW p-GROUPS AND p-GROUPS
§ 1. The Sylow Theorem.135
§ 2. Theorems on Sylow p-Groups.138
§ 3. On p-Groups .139
§ 4. On the Enumeration Theorems of the Theory of p-Groups .... 152
§ 5. On the Descending Central Series.155
§ 6. Hamiltonian Groups .159
§ 7. Applications of Extension Theory.161
V. Transfers into a subgroup
§ 1. Monomial Representation and Transfers into a Subgroup.164
§ 2. The Theorems of Burnside and Grim.169
§ 3. Groups whose Sylow Groups are All Cyclic.174
§ 4. The Principal Ideal Theorem.176
Appendixes
A. Further Exercises for Chap. II.181
B. Structure Theory and Direct Products. A Treatment of
Chap. Ill, § 2 on the Lattice-Theoretical Level.188
C. Free Products and Groups Given by a Set of Generators and
a System of Defining Relations.217
D. Further Exercises for Chap. Ill .230
E. Further Exercises for Chap. IV, § 5.238
F. Further Exercises for Chap. IV., § 1.243
G. A Theorem of Wielandt. An Addendum to Chap. IV.245
H. Further Exercises for Chap. V, § 1 .252
Frequently used symbols.253
Bibliography .255
Author Index .259
Index ..259
