Permutation Groups and Cartesian Decompositions

Cheryl E. Praeger, Csaba Schneider

• Publisher: Cambridge University Press
• Year: 2018
• Print ISBN: 9780521675062
• eBook ISBN: 9781108620239
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

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.

Table of contents

• Cover
• Series page
• Title page
• Copyright information
• Dedication page
• Table of contents
• Preface
• 1 Introduction
• Part I Permutation groups: Fundamentals
• Part II Innately transitive groups: Factorisations and cartesian decompositions
• Part III Cartesian decompositions: Applications
• Appendix Factorisations of simple and characteristically simple groups
• References
• Glossary
• Index