Classical finite transformation semigroups: An introduction

Olexandr Ganyushkin, Volodymyr Mazorchuk (auth.)9781848002807, 9781848002814, 1848002807

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 :
Front Matter….Pages i-xii
Ordinary and Partial Transformations….Pages 1-14
The Semigroups T n , PT n , and IS n ….Pages 15-38
Generating Systems….Pages 39-43
Ideals and Green ‘ s Relations….Pages 45-67
Subgroups and Subsemigroups….Pages 69-89
Other Relations on Semigroups….Pages 91-110
Endomorphisms….Pages 111-129
Nilpotent Subsemigroups….Pages 131-152
Presentation….Pages 153-174
Transitive Actions….Pages 175-188
Linear Representations….Pages 189-213
Cross-Sections….Pages 215-236
Variants….Pages 237-250
Order-Related Subsemigroups….Pages 251-275
Back Matter….Pages 277-314