Permutation Groups and Cartesian Decompositions Graphes

Cheryl e. praeger (author)|csaba schneider (author)

334 pages, parution le 30/05/2018

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Résumé

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.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.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.IllustrationsQA175Permutation groups.1EnglandCambridgeCheryl E. Praeger, Csaba Schneider.London Mathematical Society Lecture Note Series449

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Cheryl e. praeger (author)\|csaba schneider (author)
Parution	30/05/2018
Nb. de pages	334
Format	152 x 228
Poids	500g
EAN13	9780521675062

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Permutation Groups and Cartesian Decompositions Graphes

Résumé

Caractéristiques techniques

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