Permutation Groups and Cartesian Decompositions

ISBN-13: 9780521675062 / Angielski / Miękka / 2018 / 334 str.

Cheryl E. Praeger; Csaba Schneider

Opis

Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.

Recenzje

'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

Spis treści

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.