The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed, first of all, to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but should also prove useful to tutors and researchers.
Table of Contents
Ordinary and Partial Transformations.- The Semigroups T n, PT n, and IS n.- Generating Systems.- Ideals and Green ' s Relations.- Subgroups and Subsemigroups.- Other Relations on Semigroups.- Endomorphisms.- Nilpotent Subsemigroups.- Presentation.- Transitive Actions.- Linear Representations.- Cross-Sections.- Variants.- Order-Related Subsemigroups.