Classical finite transformation semigroups: an introduction

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 onthe 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 also to tutors and researchers. First book about transformation semigroups First book presenting results from former Soviet Union semigroup schools Easy to read, although fully detailed with many examples Can beused both as an introduction to transformation semigroups and abstract semigroups Has many historical remarks and open questions for further research INDICE: Preface.- 1. Ordinary and partial transformations.- 2. The semigroups Tn, PT n and ISn.- 3. Generating Systems.- 4. Ideals and Green's relations.- 5. Subgroups and subsemigroups.- 6. Other relations on semigroups.- 7. Endomorphisms.- 8. Nilpotent subsemigroups.- 9. Presentation.- 10. Transitive actions.- 11. Linear representations.- 12. Cross-sections.- 13. Variants.- 14. Order-related subsemigroups.- Answers and hints to exercises.- Bibliography.- List of notation.- Index.

• ISBN: 978-1-84800-280-7
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 335
• Fecha Publicación: 01/09/2008
• Nº Volúmenes: 1
• Idioma: Inglés