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.
General
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