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Permutation Groups [[electronic resource] /] / by John D. Dixon, Brian Mortimer
| Permutation Groups [[electronic resource] /] / by John D. Dixon, Brian Mortimer |
| Autore | Dixon John D |
| Edizione | [1st ed. 1996.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1996 |
| Descrizione fisica | 1 online resource (XII, 348 p.) |
| Disciplina | 512.66 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
K-theory
K-Theory |
| ISBN | 1-4612-0731-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. The Basic Ideas -- 1.1. Symmetry -- 1.2. Symmetric Groups -- 1.3. Group Actions -- 1.4. Orbits and Stabilizers -- 1.5. Blocks and Primitivity -- 1.6. Permutation Representations and Normal Subgroups -- 1.7. Orbits and Fixed Points -- 1.8. Some Examples from the Early History of Permutation Groups -- 1.9. Notes -- 2. Examples and Constructions -- 2.1. Actions on k-tuples and Subsets -- 2.2. Automorphism Groups of Algebraic Structures -- 2.3. Graphs -- 2.4. Relations -- 2.5. Semidirect Products -- 2.6. Wreath Products and Imprimitive Groups -- 2.7. Primitive Wreath Products -- 2.8. Affine and Projective Groups -- 2.9. The Transitive Groups of Degree at Most 7 -- 2.10. Notes -- 3. The Action of a Permutation Group -- 3.1. Introduction -- 3.2. Orbits of the Stabilizer -- 3.3. Minimal Degree and Bases -- 3.4. Frobenius Groups -- 3.5. Permutation Groups Which Contain a Regular Subgroup -- 3.6. Computing in Permutation Groups -- 3.7. Notes -- 4. The Structure of a Primitive Group -- 4.1. Introduction -- 4.2. Centralizers and Normalizers in the Symmetric Group -- 4.3. The Socle -- 4.4. Subnormal Subgroups and Primitive Groups -- 4.5. Constructions of Primitive Groups with Nonregular Socles -- 4.6. Finite Primitive Groups with Nonregular Socles -- 4.7. Primitive Groups with Regular Socles -- 4.8. Applications of the O’Nan-Scott Theorem -- 4.9. Notes -- 5. Bounds on Orders of Permutation Groups -- 5.1. Orders of Elements -- 5.2. Subgroups of Small Index in Finite Alternating and Symmetric Groups -- 5.3. The Order of a Simply Primitive Group -- 5.4. The Minimal Degree of a 2-transitive Group -- 5.5. The Alternating Group as a Section of a Permutation Group -- 5.6. Bases and Orders of 2-transitive Groups -- 5.7. The Alternating Group as a Section of a Linear Group -- 5.8. Small Subgroups of Sn -- 5.9. Notes -- 6. The Mathieu Groups and Steiner Systems -- 6.1. The Mathieu Groups -- 6.2. Steiner Systems -- 6.3. The Extension of AG2 (3) -- 6.4. The Mathieu Groups M 11 and M12 -- 6.5. The Geometry of PG 2 (4) -- 6.6. The Extension of PG 2 (4) and the Group M 22 -- 6.7. The Mathieu Groups M 23 and M 24 -- 6.8. The Geometry of W24 -- 6.9. Notes -- 7. Multiply Transitive Groups -- 7.1. Introduction -- 7.2. Normal Subgroups -- 7.3. Limits to Multiple Transitivity -- 7.4. Jordan Groups -- 7.5. Transitive Extensions -- 7.6. Sharply k-transitive Groups -- 7.7. The Finite 2-transitive Groups -- 7.8. Notes -- 8. The Structure of the Symmetric Groups -- 8.1. The Normal Structure of Sym(?) -- 8.2. The Automorphisms of Sym(?) -- 8.3. Subgroups of F Sym(?) -- 8.4. Subgroups of Small Index in Sym(?) -- 8.5. Maximal Subgroups of the Symmetric Groups -- 8.6. Notes -- 9. Examples and Applications of Infinite Permutation Groups -- 9.1. The Construction of a Finitely Generated Infinite p-group -- 9.2. Groups Acting on Trees -- 9.3. Highly Transitive Free Subgroups of the Symmetric Group -- 9.4. Homogeneous Groups -- 9.5. Automorphisms of Relational Structures -- 9.6. The Universal Graph -- 9.7. Notes -- Appendix A. Classification of Finite Simple Groups -- Appendix B. The Primitive Permutation Groups of Degree Less than 1000 -- References. |
| Record Nr. | UNINA-9910480733003321 |
Dixon John D
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Permutation Groups [[electronic resource] /] / by John D. Dixon, Brian Mortimer
| Permutation Groups [[electronic resource] /] / by John D. Dixon, Brian Mortimer |
| Autore | Dixon John D |
| Edizione | [1st ed. 1996.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1996 |
| Descrizione fisica | 1 online resource (XII, 348 p.) |
| Disciplina | 512.66 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
K-theory
K-Theory |
| ISBN | 1-4612-0731-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. The Basic Ideas -- 1.1. Symmetry -- 1.2. Symmetric Groups -- 1.3. Group Actions -- 1.4. Orbits and Stabilizers -- 1.5. Blocks and Primitivity -- 1.6. Permutation Representations and Normal Subgroups -- 1.7. Orbits and Fixed Points -- 1.8. Some Examples from the Early History of Permutation Groups -- 1.9. Notes -- 2. Examples and Constructions -- 2.1. Actions on k-tuples and Subsets -- 2.2. Automorphism Groups of Algebraic Structures -- 2.3. Graphs -- 2.4. Relations -- 2.5. Semidirect Products -- 2.6. Wreath Products and Imprimitive Groups -- 2.7. Primitive Wreath Products -- 2.8. Affine and Projective Groups -- 2.9. The Transitive Groups of Degree at Most 7 -- 2.10. Notes -- 3. The Action of a Permutation Group -- 3.1. Introduction -- 3.2. Orbits of the Stabilizer -- 3.3. Minimal Degree and Bases -- 3.4. Frobenius Groups -- 3.5. Permutation Groups Which Contain a Regular Subgroup -- 3.6. Computing in Permutation Groups -- 3.7. Notes -- 4. The Structure of a Primitive Group -- 4.1. Introduction -- 4.2. Centralizers and Normalizers in the Symmetric Group -- 4.3. The Socle -- 4.4. Subnormal Subgroups and Primitive Groups -- 4.5. Constructions of Primitive Groups with Nonregular Socles -- 4.6. Finite Primitive Groups with Nonregular Socles -- 4.7. Primitive Groups with Regular Socles -- 4.8. Applications of the O’Nan-Scott Theorem -- 4.9. Notes -- 5. Bounds on Orders of Permutation Groups -- 5.1. Orders of Elements -- 5.2. Subgroups of Small Index in Finite Alternating and Symmetric Groups -- 5.3. The Order of a Simply Primitive Group -- 5.4. The Minimal Degree of a 2-transitive Group -- 5.5. The Alternating Group as a Section of a Permutation Group -- 5.6. Bases and Orders of 2-transitive Groups -- 5.7. The Alternating Group as a Section of a Linear Group -- 5.8. Small Subgroups of Sn -- 5.9. Notes -- 6. The Mathieu Groups and Steiner Systems -- 6.1. The Mathieu Groups -- 6.2. Steiner Systems -- 6.3. The Extension of AG2 (3) -- 6.4. The Mathieu Groups M 11 and M12 -- 6.5. The Geometry of PG 2 (4) -- 6.6. The Extension of PG 2 (4) and the Group M 22 -- 6.7. The Mathieu Groups M 23 and M 24 -- 6.8. The Geometry of W24 -- 6.9. Notes -- 7. Multiply Transitive Groups -- 7.1. Introduction -- 7.2. Normal Subgroups -- 7.3. Limits to Multiple Transitivity -- 7.4. Jordan Groups -- 7.5. Transitive Extensions -- 7.6. Sharply k-transitive Groups -- 7.7. The Finite 2-transitive Groups -- 7.8. Notes -- 8. The Structure of the Symmetric Groups -- 8.1. The Normal Structure of Sym(?) -- 8.2. The Automorphisms of Sym(?) -- 8.3. Subgroups of F Sym(?) -- 8.4. Subgroups of Small Index in Sym(?) -- 8.5. Maximal Subgroups of the Symmetric Groups -- 8.6. Notes -- 9. Examples and Applications of Infinite Permutation Groups -- 9.1. The Construction of a Finitely Generated Infinite p-group -- 9.2. Groups Acting on Trees -- 9.3. Highly Transitive Free Subgroups of the Symmetric Group -- 9.4. Homogeneous Groups -- 9.5. Automorphisms of Relational Structures -- 9.6. The Universal Graph -- 9.7. Notes -- Appendix A. Classification of Finite Simple Groups -- Appendix B. The Primitive Permutation Groups of Degree Less than 1000 -- References. |
| Record Nr. | UNINA-9910789344703321 |
|
Dixon John D
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||