Classical Finite Transformation Semigroups An Introduction /

• Main Authors: Ganyushkin, Olexandr. (Author), Mazorchuk, Volodymyr. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: London : Springer London : Imprint: Springer, 2009.
• Series: Algebra and Applications, 9
• Subjects: Mathematics.; Group theory.; Combinatorics.; Group Theory and Generalizations.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-84800-281-4

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 semigrou...

Table of Contents:

• 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.