Ordered Groups And Infinite Permutation Groups

The separate areas of Ordered Groups and Infinite Permutation Groups began to converge in significant ways about thirty years ago. Since then, the connection has steadily grown so that now permutation groups are essential to many who work in ordered groups. Ordered groups are of some interest to most of those who work in infinite permutation groups, and there are a number of mathematicians whose main work is exactly in ordered permutation groups, the combination of the two. This book represents the happy confluence of the two subjects, running the spectrum from purely infinite permutation groups through ordered permutation groups to purely ordered groups. Experts in various aspects of these subjects have each contributed a chapter. The articles are surveys of recent and past work in the area and they include extensive bibliographies. Topics include lattice-ordered groups, ordered permutation groups, Jordan groups, reconstruction problems, groups with few orbits, the separation theorem, and automorphisms of symmetric groups. This book is an essential reference for anyone working in ordered groups or infinite permutation groups.