Almost completely decomposable groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Gordon and Breach
2000
|
| Schriftenreihe: | Algebra, logic and applications
13 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 354 S. graph. Darst. |
| ISBN: | 9056992252 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804127880929607680 |
|---|---|
| adam_text | Contents
Introduction 1
Acknowledgements 4
1. Notation and Background 5
1.1. Generalities 5
1.2. Rational Groups 6
1.3. The Anatomy of Finite Posets 13
1.4. Unit Groups 17
1.5. Integal Linear Algebra 19
1.6. Exercises 23
1.7. Solutions to Exercises 25
2. Basics and Completely Decomposable Groups 27
2.1. Rank, Coefficient Groups, and Purity 27
2.2. Rank One Groups and Types 30
2.3. Socles and Radicals 32
2.4. Completely Decomposable Groups 36
2.5. Bounded Quotients of Completely Decomposable Groups 43
2.6. Homocyclic Finite Groups 49
2.7. Exercises 51
2.8. Questions 57
2.9. Solutions to Exercises 57
3. Cyclic Essential Extensions 63
3.1. Cyclic Essential Extensions 63
3.2. Examples 65
3.3. Exercises 70
4. Regulating Subgroups and Regulators 73
4.1. Butler Groups 74
vii
viii CONTENTS
4.2. Regulating Subgroups 78
4.3. Counting Regulating Subgroups 85
4.4. The Regulator 87
4.5. Odds and Ends 93
4.6. Exercises 98
4.7. Questions 100
4.8. Solutions to Exercises 101
§. Local Global Relationships 103
5.1. Primary Constituents 103
5.2. Localization of the Regulator Criterion 106
5.3. Regulating Subgroups of Primary Constituents 107
5.4. Questions 108
6. Groups with Cyclic Regulating Quotient 109
6.1. Notation and Basics 110
6.2. Regulating Subgoups 111
6.3. Clipped crq Groups 114
6.4. Local crq Groups 118
6.5. Direct Decomposition of Local crq Groups 119
6.6. Regulating Quotients of Local crq Groups 127
6.7. Exercises 133
6.8. Questions 136
6.9. Solutions to Exercises 136
7. Completely Decomposable Summands 141
7.1. Width and Rank 141
7.2. Radicals and Co Butler Decompositions 143
7.3. Completely Decomposable Summands and Clipped
Groups 146
7.4. Exercises 151
7.5. Questions 152
7.6. Solutions to Exercises 153
8. Anti Representations 155
8.1. Anti Representations 156
8.2. Isomorphism 161
8.3. Exercises 169
8.4. Solutions to Exercises 170
9. Near Isomorphism and Type Isomorphism 171
9.1 Near Isomorphism 171
CONTENTS ix
9.2. Type Isomorphism is Near Isomorphism 176
9.3. Exercises 181
9.4. Questions 181
9.5. Solutions to Exercises 182
10. Fundamental Decomposition Theorems 185
10.1. Lifting Idempotents 186
10.2. Arnold s Theorem 189
10.3. The Azumaya Theorem 192
10.4. The Faticoni Schultz Theorem 195
10.5. Exercises 197
10.6. Questions 198
10.7. Solutions to Exercises 198
11. Finite Essential Extensions 199
11.1. Standard Description 199
11.2. Greatest Common Divisors 202
11.3. Computation of Greatest Common Divisors 208
11.4. Purification of Base Group Summands 210
11.5. Burkhardt Invariants 212
11.6. Primary Constituents 214
11.7. Representing Matrices 215
11.8. Two Existence Theorems 216
11.9. Completely Decomposable Direct Summands 218
11.10. A Big Example and Maple Procedures 221
11.11. Some Additional Maple Procedures 237
11.12. Exercises 238
11.13. Questions 242
11.14. Solutions to Exercises 242
12. Classification 249
12.1. crq Group 249
12.2. Near Isomorphism Invariants 252
12.3. Two Critical Types 254
12.4. Homocyclic Regulator Quotients 257
12.5. Uniform Groups 259
12.6. Global Block Rigid crq Groups and Isomorphism 264
12.7. Some Applications 269
12.8. Exercises 272
12.9. Questions 276
12.10. Solutions to Exercises 276
x CONTENTS
13. Direct Decompositions of Block Rigid crq Groups 281
13.1. Decompositions 281
13.2. Exercises 292
13.3. Solutions to Exercises 292
14. In Search for Good Categories 293
14.1. Some Natural Categories 293
14.2. Categories of ACD Groups and Anti Representations 294
14.3. Exercises 299
14.4. Questions 301
14.5. Solutions to Exercises 301
15. Associated Structures 303
15.1. Endomorphism Rings of Completely Decomposable
Groups 303
15.2. Endomorphism Rings of Almost Completely
Decomposable Groups 306
15.3. Endomorphism Rings of Rigid crq Groups 307
15.4. Endomorphism Rings and Type Endomorphism Rings 312
15.5. The Structure of TypEndxA 313
15.6. Exercises 314
15.7. Questions 316
15.8. Solutions to Exercises 317
16. Literature 323
16.1. Regulating Hulls 323
16.2. Tight Subgroups 325
16.3. Pure Subgroups and Torsion Free Quotients 326
16.4. High and Low Covers 327
16.5. The Invariants of Vinsonhaler 330
16.6. The Ladder Phenomenon 332
16.7. Further Papers 333
16.8. Exercises 334
16.9. Questions 337
16.10. Solutions to Exercises 338
Bibliography 343
Index 347
|
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| indexdate | 2024-07-09T18:40:23Z |
| institution | BVB |
| isbn | 9056992252 |
| language | English |
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| physical | X, 354 S. graph. Darst. |
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| spelling | Mader, Adolf Verfasser (DE-588)117711578 aut Almost completely decomposable groups Adolf Mader Amsterdam [u.a.] Gordon and Breach 2000 X, 354 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algebra, logic and applications 13 Décomposition (Mathématiques) Décomposition (mathématiques) ram Groupes abéliens Groupes abéliens ram Abelian groups Decomposition (Mathematics) Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 s DE-604 Algebra, logic and applications 13 (DE-604)BV002639285 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008980205&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mader, Adolf Almost completely decomposable groups Algebra, logic and applications Décomposition (Mathématiques) Décomposition (mathématiques) ram Groupes abéliens Groupes abéliens ram Abelian groups Decomposition (Mathematics) Gruppe Mathematik (DE-588)4022379-6 gnd |
| subject_GND | (DE-588)4022379-6 |
| title | Almost completely decomposable groups |
| title_auth | Almost completely decomposable groups |
| title_exact_search | Almost completely decomposable groups |
| title_full | Almost completely decomposable groups Adolf Mader |
| title_fullStr | Almost completely decomposable groups Adolf Mader |
| title_full_unstemmed | Almost completely decomposable groups Adolf Mader |
| title_short | Almost completely decomposable groups |
| title_sort | almost completely decomposable groups |
| topic | Décomposition (Mathématiques) Décomposition (mathématiques) ram Groupes abéliens Groupes abéliens ram Abelian groups Decomposition (Mathematics) Gruppe Mathematik (DE-588)4022379-6 gnd |
| topic_facet | Décomposition (Mathématiques) Décomposition (mathématiques) Groupes abéliens Abelian groups Decomposition (Mathematics) Gruppe Mathematik |
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