Synopses & Reviews
This book provides a thorough account of wreath products of groups and semigroups. Wreath products have arisen in many situations in both group and semigroup theory, often providing examples of unexpected behaviour, but also in quite fundamental settings. They occur equally in many applications in science, in particular in physics and chemistry. In spite of this there has been no dedicated survey of the ideas and methods involved until this book.
As well as the two best known fundamental results, the Krasner-Kaloujnine Theorem in group theory and the Krohn-Rhodes Theorem in semigroup theory, the author presents a number of results in a variety of topics covering a wide area, but it has proved impossible to cover all topics in which wreath products have played a role. The material has been chosen to provide both an account of important work and a taste of the various techniques that arise in the theory. Several generalisations and extensions are also presented.
The presuppositions are a working knowledge of group and semigroup theory, something a little beyond the core abstract algebra course in a first degree. The material is presented in what most workers in the field would consider the most natural context: that of permutation groups and transformation semigroups. This has entailed in many cases that published material has had to be considerably generalised, so the book contains a substantial amount of original work as well as many improved proofs.
Any persons who may find wreath products of use in their work should be able to use this book to ease their job considerably. This is true both for those working in non mathematical areas such as theoretical physics and chemistry, as well as those working in mathematics, in particular algebraists.