Oligomorphic permutation groups /:
The study of permutation groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. They are precisely those structures which are determined by f...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1990.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
152. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The study of permutation groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. They are precisely those structures which are determined by first-order logical axioms together with the assumption of countability. This book concerns such structures, their substructures and their automorphism groups. A wide range of techniques are used: group theory, combinatorics, Baire category and measure among them. The book arose from lectures given at a research symposium and retains their informal style, whilst including as well many recent results from a variety of sources. It concludes with exercises and unsolved research problems. |
| Beschreibung: | 1 online resource (viii, 160 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 145-154) and index. |
| ISBN: | 9781107361638 110736163X 9780511549809 0511549806 |
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| 245 | 1 | 0 | |a Oligomorphic permutation groups / |c Peter J. Cameron. |
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 152 | |
| 504 | |a Includes bibliographical references (pages 145-154) and index. | ||
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| 520 | |a The study of permutation groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. They are precisely those structures which are determined by first-order logical axioms together with the assumption of countability. This book concerns such structures, their substructures and their automorphism groups. A wide range of techniques are used: group theory, combinatorics, Baire category and measure among them. The book arose from lectures given at a research symposium and retains their informal style, whilst including as well many recent results from a variety of sources. It concludes with exercises and unsolved research problems. | ||
| 505 | 0 | |a Cover; Title; Copyright; Preface; Contents; 1 Background; 1.1 History and notation; 1.2 Permutation groups; 1.3 Model theory; 1.4 Category and measure; 1.5 Ramsey's Theorem; 2 Preliminaries; 2.1 The objects of study; 2.2 Reduction to the countable case; 2.3 The canonical relational structure; 2.4 Topology; 2.5 The Ryll-Nardzewski Theorem; 2.6 Homogeneous structures; 2.7 Strong amalgamation; 2.8 Appendix: Two proofs; 2.9 Appendix: Quantifier elimination and model completeness; 2.10 Appendix: The random graph; 3 Examples and growth rates; 3.1 Monotonicity; 3.2 Direct and wreath products | |
| 505 | 8 | |a 3.3 Some primitive groups3.4 Homogeneity and transitivity; 3.5 fn = fn + 1; 3.6 Growth rates; 3.7 Appendix: Cycle index; 3.8 Appendix: A graded algebra; 4 Subgroups; 4.1 Beginnings; 4.2 A theorem of Macpherson; 4.3 The random graph revisited; 4.4 Measure, continued; 4.5 Category; 4.6 Multicoloured sets; 4.7 Almost all automorphisms?; 4.8 Subgroups of small index; 4.9 Normal subgroups; 4.10 Appendix: The tree of an age; 5. Miscellaneous topics; 5.1 Jordan groups; 5.2 Going forth; 5.3 No-categorical, unstable structures; 5.4 An example; 5.5 Another example; 5.6 Oligomorphic projective groups | |
| 505 | 8 | |a 5.7 Orbits on infinite setsReferences; Index | |
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| author | Cameron, Peter J. (Peter Jephson), 1947- |
| author_GND | http://id.loc.gov/authorities/names/n81072709 |
| author_facet | Cameron, Peter J. (Peter Jephson), 1947- |
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| contents | Cover; Title; Copyright; Preface; Contents; 1 Background; 1.1 History and notation; 1.2 Permutation groups; 1.3 Model theory; 1.4 Category and measure; 1.5 Ramsey's Theorem; 2 Preliminaries; 2.1 The objects of study; 2.2 Reduction to the countable case; 2.3 The canonical relational structure; 2.4 Topology; 2.5 The Ryll-Nardzewski Theorem; 2.6 Homogeneous structures; 2.7 Strong amalgamation; 2.8 Appendix: Two proofs; 2.9 Appendix: Quantifier elimination and model completeness; 2.10 Appendix: The random graph; 3 Examples and growth rates; 3.1 Monotonicity; 3.2 Direct and wreath products 3.3 Some primitive groups3.4 Homogeneity and transitivity; 3.5 fn = fn + 1; 3.6 Growth rates; 3.7 Appendix: Cycle index; 3.8 Appendix: A graded algebra; 4 Subgroups; 4.1 Beginnings; 4.2 A theorem of Macpherson; 4.3 The random graph revisited; 4.4 Measure, continued; 4.5 Category; 4.6 Multicoloured sets; 4.7 Almost all automorphisms?; 4.8 Subgroups of small index; 4.9 Normal subgroups; 4.10 Appendix: The tree of an age; 5. Miscellaneous topics; 5.1 Jordan groups; 5.2 Going forth; 5.3 No-categorical, unstable structures; 5.4 An example; 5.5 Another example; 5.6 Oligomorphic projective groups 5.7 Orbits on infinite setsReferences; Index |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:25:17Z |
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| spelling | Cameron, Peter J. (Peter Jephson), 1947- https://id.oclc.org/worldcat/entity/E39PBJr7Wp9w9KWmP9RdFyM773 http://id.loc.gov/authorities/names/n81072709 Oligomorphic permutation groups / Peter J. Cameron. Cambridge ; New York : Cambridge University Press, 1990. 1 online resource (viii, 160 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 152 Includes bibliographical references (pages 145-154) and index. Print version record. The study of permutation groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. They are precisely those structures which are determined by first-order logical axioms together with the assumption of countability. This book concerns such structures, their substructures and their automorphism groups. A wide range of techniques are used: group theory, combinatorics, Baire category and measure among them. The book arose from lectures given at a research symposium and retains their informal style, whilst including as well many recent results from a variety of sources. It concludes with exercises and unsolved research problems. Cover; Title; Copyright; Preface; Contents; 1 Background; 1.1 History and notation; 1.2 Permutation groups; 1.3 Model theory; 1.4 Category and measure; 1.5 Ramsey's Theorem; 2 Preliminaries; 2.1 The objects of study; 2.2 Reduction to the countable case; 2.3 The canonical relational structure; 2.4 Topology; 2.5 The Ryll-Nardzewski Theorem; 2.6 Homogeneous structures; 2.7 Strong amalgamation; 2.8 Appendix: Two proofs; 2.9 Appendix: Quantifier elimination and model completeness; 2.10 Appendix: The random graph; 3 Examples and growth rates; 3.1 Monotonicity; 3.2 Direct and wreath products 3.3 Some primitive groups3.4 Homogeneity and transitivity; 3.5 fn = fn + 1; 3.6 Growth rates; 3.7 Appendix: Cycle index; 3.8 Appendix: A graded algebra; 4 Subgroups; 4.1 Beginnings; 4.2 A theorem of Macpherson; 4.3 The random graph revisited; 4.4 Measure, continued; 4.5 Category; 4.6 Multicoloured sets; 4.7 Almost all automorphisms?; 4.8 Subgroups of small index; 4.9 Normal subgroups; 4.10 Appendix: The tree of an age; 5. Miscellaneous topics; 5.1 Jordan groups; 5.2 Going forth; 5.3 No-categorical, unstable structures; 5.4 An example; 5.5 Another example; 5.6 Oligomorphic projective groups 5.7 Orbits on infinite setsReferences; Index Permutation groups. http://id.loc.gov/authorities/subjects/sh85099993 Groupes de permutations. MATHEMATICS Group Theory. bisacsh Permutation groups fast Permutatiegroepen. gtt Groupes de permutations. ram Print version: Cameron, Peter J. (Peter Jephson), 1947- Oligomorphic permutation groups. Cambridge ; New York : Cambridge University Press, 1990 0521388368 (DLC) 91104659 (OCoLC)22158351 London Mathematical Society lecture note series ; 152. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552340 Volltext |
| spellingShingle | Cameron, Peter J. (Peter Jephson), 1947- Oligomorphic permutation groups / London Mathematical Society lecture note series ; Cover; Title; Copyright; Preface; Contents; 1 Background; 1.1 History and notation; 1.2 Permutation groups; 1.3 Model theory; 1.4 Category and measure; 1.5 Ramsey's Theorem; 2 Preliminaries; 2.1 The objects of study; 2.2 Reduction to the countable case; 2.3 The canonical relational structure; 2.4 Topology; 2.5 The Ryll-Nardzewski Theorem; 2.6 Homogeneous structures; 2.7 Strong amalgamation; 2.8 Appendix: Two proofs; 2.9 Appendix: Quantifier elimination and model completeness; 2.10 Appendix: The random graph; 3 Examples and growth rates; 3.1 Monotonicity; 3.2 Direct and wreath products 3.3 Some primitive groups3.4 Homogeneity and transitivity; 3.5 fn = fn + 1; 3.6 Growth rates; 3.7 Appendix: Cycle index; 3.8 Appendix: A graded algebra; 4 Subgroups; 4.1 Beginnings; 4.2 A theorem of Macpherson; 4.3 The random graph revisited; 4.4 Measure, continued; 4.5 Category; 4.6 Multicoloured sets; 4.7 Almost all automorphisms?; 4.8 Subgroups of small index; 4.9 Normal subgroups; 4.10 Appendix: The tree of an age; 5. Miscellaneous topics; 5.1 Jordan groups; 5.2 Going forth; 5.3 No-categorical, unstable structures; 5.4 An example; 5.5 Another example; 5.6 Oligomorphic projective groups 5.7 Orbits on infinite setsReferences; Index Permutation groups. http://id.loc.gov/authorities/subjects/sh85099993 Groupes de permutations. MATHEMATICS Group Theory. bisacsh Permutation groups fast Permutatiegroepen. gtt Groupes de permutations. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85099993 |
| title | Oligomorphic permutation groups / |
| title_auth | Oligomorphic permutation groups / |
| title_exact_search | Oligomorphic permutation groups / |
| title_full | Oligomorphic permutation groups / Peter J. Cameron. |
| title_fullStr | Oligomorphic permutation groups / Peter J. Cameron. |
| title_full_unstemmed | Oligomorphic permutation groups / Peter J. Cameron. |
| title_short | Oligomorphic permutation groups / |
| title_sort | oligomorphic permutation groups |
| topic | Permutation groups. http://id.loc.gov/authorities/subjects/sh85099993 Groupes de permutations. MATHEMATICS Group Theory. bisacsh Permutation groups fast Permutatiegroepen. gtt Groupes de permutations. ram |
| topic_facet | Permutation groups. Groupes de permutations. MATHEMATICS Group Theory. Permutation groups Permutatiegroepen. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552340 |
| work_keys_str_mv | AT cameronpeterj oligomorphicpermutationgroups |