The theory of groups / by Hans J. Zassenhaus.
Editor: New York : Chelsea, c1958Edición: 2nd edDescripción: x, 265 p. ; cmOtra clasificación: 20-01CONTENTS 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. Normalizer, 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 [183] 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. III, § 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. III [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]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|---|
Libros
|
Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 20 Z38 (Browse shelf) | Available | A-545 |
Incluye referencias bibliográficas (p. 255-258) e índice.
CONTENTS --
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. Normalizer, 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 [183] --
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. III, § 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. III [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] --
MR, 19,939d
Click on an image to view it in the image viewer
There are no comments on this title.