Partially ordered groups
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1999
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| Schriftenreihe: | Series in algebra
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Partially ordered groups |c A. M. W. Glass |
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| 300 | |a XIII, 307 S. | ||
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008679715 | |
Datensatz im Suchindex
| _version_ | 1819781747662913536 |
|---|---|
| adam_text | CONTENTS
1 Definitions and Examples 1
1.1 Right partially ordered groups 1
1.2 Partially ordered groups 2
1.3 Examples 2
2 Basic Properties 15
2.1 Basic group theoretic properties 15
2.2 Orderability 18
2.3 Basic order theoretic properties 20
2.4 Characterisations of classes 24
3 Values, Primes and Polars 31
3.1 Values 31
3.2 Homomorphisms 34
3.3 Prime subgroups 36
3.4 Special values 39
3.5 Polars 41
3.6 Closed subgroups 44
3.7 A limiting example 49
3.8 Residually ordered groups 51
3.9 Finite pairwise orthogonal sets 53
4 Abelian and Normal valued Lattice ordered Groups 55
4.1 Simple Abelian lattice ordered groups 55
4.2 Normal valued lattice ordered groups 58
4.3 Special valued lattice ordered groups 63
4.4 Archimedean lattice ordered groups 65
4.5 Hahn s Theorem 69
xi
xii CONTENTS
4.6 The Conrad Harvey Holland Theorem 73
4.7 Elementary theory (Abelian ^ groups) 75
5 Archimedean Function Groups 87
5.1 Free Abelian lattice ordered groups 87
5.2 Finitely presented Abelian £ groups 88
5.3 The Isomorphism Problem 91
5.4 Free products of Abelian ^ groups 92
5.5 Kaplansky s Example 94
5.6 Bernau s Theorem 95
5.7 The Spectrum 103
5.8 Hyperarchimedean ^ groups 104
6 Soluble Right Partially Ordered Groups : Generalisa¬
tions 107
6.1 Nilpotent lattice ordered groups 107
6.2 The Engel Condition 109
6.3 The Word Problem 113
6.4 Weakly Abelian ^ groups 116
6.5 Divisibility 118
6.6 Conrad right orders 120
6.7 Local nilpotency 123
6.8 4 Engel right ordered groups 124
6.9 Local indicability 127
6.10 Two sided right orders 133
7 Permutations 139
7.1 The Cay ley Holland Theorem 139
7.2 Amalgamation 144
7.3 Convex blocks and congruences 145
7.4 Primitive permutation groups 146
7.5 Primitive components 154
7.6 The Wreath product 156
8 Applications 163
8.1 Normal valued ^ permutation groups 163
8.2 Nilpotent relations and soluble identities 165
8.3 Conjugacy 169
CONTENTS xiii
8.4 Free lattice ordered groups 170
8.5 Free products of f groups 175
8.6 Simple lattice ordered groups 177
8.7 Finitely presented ^ groups 182
8.8 Undecidable Problems 184
9 Completions 191
9.1 Complete partially ordered groups 191
9.2 ^ convergence structures 195
9.3 The Order completion 199
9.4 Special closure 204
9.5 Iterated Cauchy closure 206
9.6 The lateral completion 209
9.7 The distinguished completion 214
10 Varieties of Lattice ordered Groups 227
10.1 Definitions and Examples 227
10.2 General facts 229
10.3 Minimal maximal proper varieties 230
10.4 Socle 232
10.5 Powers of A 235
10.6 Dimension theory 238
10.7 Powers of U 240
10.8 Covers of A 247
10.9 The number of varieties 258
11 Unsolved Problems 261
REFERENCES 267
FURTHER SUGGESTED READING 275
LIST OF SYMBOLS 299
INDEX 301
|
| any_adam_object | 1 |
| author | Glass, A. M. W. 1944- |
| author_GND | (DE-588)172099129 |
| author_facet | Glass, A. M. W. 1944- |
| author_role | aut |
| author_sort | Glass, A. M. W. 1944- |
| author_variant | a m w g amw amwg |
| building | Verbundindex |
| bvnumber | BV012764959 |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)440879980 (DE-599)BVBBV012764959 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012764959 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T15:11:25Z |
| institution | BVB |
| isbn | 9810234937 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008679715 |
| oclc_num | 440879980 |
| open_access_boolean | |
| owner | DE-739 DE-703 |
| owner_facet | DE-739 DE-703 |
| physical | XIII, 307 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in algebra |
| series2 | Series in algebra |
| spellingShingle | Glass, A. M. W. 1944- Partially ordered groups Series in algebra Geordnete Gruppe (DE-588)4156745-6 gnd |
| subject_GND | (DE-588)4156745-6 |
| title | Partially ordered groups |
| title_auth | Partially ordered groups |
| title_exact_search | Partially ordered groups |
| title_full | Partially ordered groups A. M. W. Glass |
| title_fullStr | Partially ordered groups A. M. W. Glass |
| title_full_unstemmed | Partially ordered groups A. M. W. Glass |
| title_short | Partially ordered groups |
| title_sort | partially ordered groups |
| topic | Geordnete Gruppe (DE-588)4156745-6 gnd |
| topic_facet | Geordnete Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008679715&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010096634 |
| work_keys_str_mv | AT glassamw partiallyorderedgroups |