Notes on infinite permutation groups:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Schriftenreihe: | Lecture notes in mathematics
1698 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 202 S. graph. Darst. |
| ISBN: | 3540649654 |
Internformat
MARC
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| 245 | 1 | 0 | |a Notes on infinite permutation groups |c M. Bhattacharjee ... |
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| 490 | 1 | |a Lecture notes in mathematics |v 1698 | |
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Datensatz im Suchindex
| _version_ | 1804126843982315520 |
|---|---|
| adam_text | Contents
1 Some Group Theory i
2 Groups acting on Sets 9
2.1 Group actions 9
2.2 Permutation groups 11
2.3 Cycles and cycle types 14
2.4 Basic facts about symmetric groups 16
3 Transitivity 19
3.1 Orbits and transitivity 19
3.2 Stabilisers and transitivity 21
3.3 Extensions of transitivity 23
3.4 Homogeneity 26
4 Primitivity 31
4.1 G congruences 31
4.2 Primitive spaces 33
4.3 Extensions of primitivity 37
5 Suborbits and Orbitals 39
5.1 Suborbits and orbitals 39
5.2 Orbital graphs and primitivity 41
6 More about Symmetric Groups 49
6.1 Normal subgroups of symmetric groups 50
6.2 Groups with finitary permutations 52
7 Linear Groups 57
7.1 General Linear Groups 57
ix
7.2 Projective groups 61
7.3 Affine groups 63
7.4 Projective and affine spaces 65
8 Wreath Products 67
8.1 Definition 67
8.2 Wreath products as permutation groups 70
8.3 Imprimitivity of wreath products 71
8.4 Variations of wreath products 74
9 Rational Numbers 77
9.1 Cantor s Theorem 77
9.2 Back and forth ? s going forth 81
9.3 Order automorphisms of the rationals 82
10 Jordan Groups 87
10.1 Definitions and some examples 87
10.2 Basic properties of Jordan sets 88
10.3 More properties of Jordan sets 90
10.4 Cofinite Jordan sets 94
11 Examples of Jordan Groups 99
11.1 Some examples 99
11.1.1 Finite primitive examples 99
11.1.2 Highly transitive examples 100
11.2 Linear groups and Steiner systems 101
11.3 Linear relational structures 104
11.3.1 Linear order 105
11.3.2 Linear betweenness relation 107
11.3.3 Circular order 108
11.3.4 Separation relation 110
12 Relations related to betweenness 115
12.1 Semilinear order 115
12.2 C relations 121
12.3 General betweenness relations 124
12.4 /^ relations 126
12.5 Primitive groups with primitive Jordan sets 128
13 Classification Theorems 131
13.1 Statement of the theorems 131
13.2 Some recognition theorems 135
13.3 Some basic lemmas 138
13.4 Outline of the proof of Theorem 13.3 140
14 Homogeneous Structures 143
14.1 Some model theory 143
14.2 Building homogeneous structures 147
14.3 Examples of homogeneous structures 152
14.4 Proof of Frai sse s Theorem 155
15 The Hrushovski Construction 159
15.1 Generalisation of Frai sse s Theorem 159
15.2 Building a geometry 161
15.3 Extending the geometry 166
16 Applications and Open Questions 171
16.1 Bounded groups 171
16.2 Cycle types 172
16.3 Strictly minimal sets 174
16.4 Back and forth arguments 176 ,
16.5 Homogeneous structures 177
16.6 Structure of Jordan groups 177
16.7 Generalisations of Jordan groups 180
Bibliography 181
List of Symbols 189
Index 195
|
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| indexdate | 2024-07-09T18:23:54Z |
| institution | BVB |
| isbn | 3540649654 |
| language | German |
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| physical | XI, 202 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Notes on infinite permutation groups M. Bhattacharjee ... Berlin [u.a.] Springer 1998 XI, 202 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1698 Algebra larpcal Groupes de permutations Permutatiegroepen gtt Permutation groups Permutationsgruppe (DE-588)4173833-0 gnd rswk-swf Unendliche Gruppe (DE-588)4375539-2 gnd rswk-swf Permutationsgruppe (DE-588)4173833-0 s DE-604 Unendliche Gruppe (DE-588)4375539-2 s Bhattacharjee, Meenaxi 1965- Sonstige (DE-588)120374447 oth Lecture notes in mathematics 1698 (DE-604)BV000676446 1698 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008285278&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Notes on infinite permutation groups Lecture notes in mathematics Algebra larpcal Groupes de permutations Permutatiegroepen gtt Permutation groups Permutationsgruppe (DE-588)4173833-0 gnd Unendliche Gruppe (DE-588)4375539-2 gnd |
| subject_GND | (DE-588)4173833-0 (DE-588)4375539-2 |
| title | Notes on infinite permutation groups |
| title_auth | Notes on infinite permutation groups |
| title_exact_search | Notes on infinite permutation groups |
| title_full | Notes on infinite permutation groups M. Bhattacharjee ... |
| title_fullStr | Notes on infinite permutation groups M. Bhattacharjee ... |
| title_full_unstemmed | Notes on infinite permutation groups M. Bhattacharjee ... |
| title_short | Notes on infinite permutation groups |
| title_sort | notes on infinite permutation groups |
| topic | Algebra larpcal Groupes de permutations Permutatiegroepen gtt Permutation groups Permutationsgruppe (DE-588)4173833-0 gnd Unendliche Gruppe (DE-588)4375539-2 gnd |
| topic_facet | Algebra Groupes de permutations Permutatiegroepen Permutation groups Permutationsgruppe Unendliche Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008285278&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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