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.
Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.
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.
'This is a thorough reference book that consists of three parts ...
In summary, the book is an impressive collection of theorems and
their proofs.' Miklos Bona, MAA Reviews
'One of the most important achievements of this book is building the first formal theory on G-invariant cartesian decompositions; this brings to the fore a better knowledge of the O'Nan-Scott theorem for primitive, quasiprimitive, and innately transitive groups, together with the embeddings among these groups. This is a valuable, useful, and beautiful book.' Pablo Spiga, Mathematical Reviews