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Permutation Groups and Cartesian Decompositions

Buch | Softcover
334 Seiten
2018
Cambridge University Press (Verlag)
978-0-521-67506-2 (ISBN)
CHF 127,40 inkl. MwSt
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The theory of permutation groups has a wide range of applications including combinatorics, graph theory, computer science, theoretical physics and molecular chemistry. This book introduces topics that will appeal to students and researchers who require knowledge of permutation group theory for their work and are interested in its applications.
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.

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. Csaba Schneider is Professor in the Maths Department at the Federal University of Minas Gerais, Brazil. He has held research positions at the University of Western Australia, Perth, the Technical University of Braunschweig, the Hungarian Academy of Sciences, and the University of Lisbon. His mathematical interests include finite group theory, the theory of non-associative algebras, and computational algebra.

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.

Reihe/Serie London Mathematical Society Lecture Note Series
Zusatzinfo Worked examples or Exercises; 14 Tables, black and white; 2 Line drawings, black and white
Verlagsort Cambridge
Sprache englisch
Maße 151 x 227 mm
Gewicht 500 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Graphentheorie
Schlagworte London Mathematical Society Lecture Note
ISBN-10 0-521-67506-5 / 0521675065
ISBN-13 978-0-521-67506-2 / 9780521675062
Zustand Neuware
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