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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1990.
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| Colección: | London Mathematical Society lecture note series ;
152. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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