Permutation Groups and Cartesian Decompositions

By: Cheryl E. Praeger, Csaba Schneider

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Paperback | 3 May 2018

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338 Pages

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15.1 x 22.9 x 2.6

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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'Nanâ"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.

Industry Reviews

'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

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