Cheryl E. Praeger

Permutation Groups and Cartesian Decompositions (eBook, ePUB)

• Format: ePub

Produktbeschreibung

Permutation groups, their fundamental theory and applications are discussed in this introductory book. It focuses on those groups that are most useful for studying symmetric structures such as graphs, codes and designs. Modern treatments of the O'Nan-Scott theory are presented not only for primitive permutation groups but also for the larger families of quasiprimitive and innately transitive groups, including several classes of infinite permutation groups. Their precision is sharpened by the introduction of a cartesian decomposition concept. This facilitates reduction arguments for primitive groups analogous to those, using orbits and partitions, that reduce problems about general permutation groups to primitive groups. The results are particularly powerful for finite groups, where the finite simple group classification is invoked. Applications are given in algebra and combinatorics to group actions that preserve cartesian product structures. Students and researchers with an interest in mathematical symmetry will find the book enjoyable and useful.

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Produktdetails

• Verlag: Cambridge University Press
• Englisch
• ISBN-13: 9781316999059
• Artikelnr.: 53273939

Autorenporträt

Cheryl E. Praeger is Emeritus Professor at the Centre for the Mathematics of Symmetry and Computation at the University of Western Australia, Perth. She is an Honorary Life Member of the Australian Mathematical Society, and was its first female President. She has authored more than 400 research publications, including five books. Besides holding honorary doctorates awarded by universities in Thailand, Iran, Belgium, Scotland, and Australia, she is also a member of the Order of Australia for her service to mathematics in Australia.

Inhaltsangabe

1. Introduction
Part I. Permutation Groups - Fundamentals: 2. Group actions and permutation groups
3. Minimal normal subgroups of transitive permutation groups
4. Finite direct products of groups
5. Wreath products
6. Twisted wreath products
7. O'Nan-Scott theory and the maximal subgroups of finite alternating and symmetric groups
Part II. Innately Transitive Groups - Factorisations and Cartesian Decompositions: 8. Cartesian factorisations
9. Transitive cartesian decompositions for innately transitive groups
10. Intransitive cartesian decompositions
Part III. Cartesian Decompositions - Applications: 11. Applications in permutation group theory
12. Applications to graph theory
Appendix. Factorisations of simple and characteristically simple groups
Glossary
References
Index.