The theory of groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English German |
| Veröffentlicht: |
New York
Chelsea Publ. Co.
1958
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 265 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a The theory of groups |
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Datensatz im Suchindex
| _version_ | 1804118292836646912 |
|---|---|
| adam_text | 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
ix
x Contents
§ 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 Denning 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
|
| any_adam_object | 1 |
| author | Zassenhaus, Hans 1912-1991 |
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| author_facet | Zassenhaus, Hans 1912-1991 |
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| author_sort | Zassenhaus, Hans 1912-1991 |
| author_variant | h z hz |
| building | Verbundindex |
| bvnumber | BV004062372 |
| callnumber-first | Q - Science |
| callnumber-label | QA171 |
| callnumber-raw | QA171 |
| callnumber-search | QA171 |
| callnumber-sort | QA 3171 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)556027 (DE-599)BVBBV004062372 |
| dewey-full | 512.86 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.86 |
| dewey-search | 512.86 |
| dewey-sort | 3512.86 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:07:59Z |
| institution | BVB |
| language | English German |
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| physical | X, 265 S. |
| publishDate | 1958 |
| publishDateSearch | 1958 |
| publishDateSort | 1958 |
| publisher | Chelsea Publ. Co. |
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| spelling | Zassenhaus, Hans 1912-1991 Verfasser (DE-588)119439204 aut Lehrbuch der Gruppentheorie The theory of groups 2. ed. New York Chelsea Publ. Co. 1958 X, 265 S. txt rdacontent n rdamedia nc rdacarrier Groupes, Théorie des Teoria Dos Grupos larpcal Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002540334&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zassenhaus, Hans 1912-1991 The theory of groups Groupes, Théorie des Teoria Dos Grupos larpcal Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4072157-7 |
| title | The theory of groups |
| title_alt | Lehrbuch der Gruppentheorie |
| title_auth | The theory of groups |
| title_exact_search | The theory of groups |
| title_full | The theory of groups |
| title_fullStr | The theory of groups |
| title_full_unstemmed | The theory of groups |
| title_short | The theory of groups |
| title_sort | the theory of groups |
| topic | Groupes, Théorie des Teoria Dos Grupos larpcal Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Groupes, Théorie des Teoria Dos Grupos Group theory Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002540334&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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