Articoli correlati a Permutation Groups: 163
Sinossi
The study of permutation groups has always been an integral part of group theory. Permutation groups are important as a tool for solving group theoretic and combinatorial problems, and as a source of significant examples of groups. The reader is assumed to have had a first course in group theory. Numerous examples and exercises make the book suitable both as a course text and for self-study.
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Contenuti
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.
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Book by Dixon John D Mortimer Brian
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Permutation Groups (Graduate Texts in Mathematics)
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Permutation Groups
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Following the basic ideas, standard constructions and important examples in the theory of permutation groups, the book goes on to develop the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal ONan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. With its many exercises and detailed references to the current literature, this text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, as well as for self-study. 364 pp. Englisch. Codice articolo 9781461268857
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Permutation Groups
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Permutation Groups
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Following the basic ideas, standard constructions and important examples in the theory of permutation groups, the book goes on to develop the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal ONan-Scott Theo. Codice articolo 4189521
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Permutation Groups
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Permutation Groups form one of the oldest parts of group theory. Through the ubiquity of group actions and the concrete representations which they afford, both finite and infinite permutation groups arise in many parts of mathematics and continue to be a lively topic of research in their own right. The book begins with the basic ideas, standard constructions and important examples in the theory of permutation groups.It then develops the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal O'Nan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. This text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, or for self- study. It includes many exercises and detailed references to the current literature.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 364 pp. Englisch. Codice articolo 9781461268857
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Permutation Groups
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Springer New York, Springer US, 2012
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - Permutation Groups form one of the oldest parts of group theory. Through the ubiquity of group actions and the concrete representations which they afford, both finite and infinite permutation groups arise in many parts of mathematics and continue to be a lively topic of research in their own right. The book begins with the basic ideas, standard constructions and important examples in the theory of permutation groups.It then develops the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal O'Nan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. This text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, or for self- study. It includes many exercises and detailed references to the current literature. Codice articolo 9781461268857
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Permutation Groups (Graduate Texts in Mathematics, 163)
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