Generators and ranks of transformation semigroups

ABSTRACTMSc THESISGENERATORS AND RANK OF TRANSFORMATION SEMIGROUPSMetin KOCşDEPARTMENT OF MATHEMATICSINSTITUTE OF NATURAL AND APPLIED SCIENCESUNIVERSITY OF CUKUROVAşSupervisor: Assoc.Prof.Dr. Hayrullah AYIKYear: 2005, Pages: 43Jury: Assoc.Prof.Dr. Hayrullah AYIKü üProf.Dr. Yusuf UNLUAssist.Prof.Dr. Ersin KIRALIn this study, we gather some theorems about the generators of some transformationsemigroups playing an important role in semigroup theory. Such as we gave a minimalgenerating set and the rank of finite full transformation semigroup. Also the structure ofpartial transformation semigroup which includes the transformation semigroup was given.The subsemigroup generated by idempotent elements of finite transformation semigroupand properties of this idempotent elements are presented. Finally, order preserving transfor-mation semigroup which is a subsemigroup of the transformation semigroup was defined,the structure and some generators of these transformations were given.Key Words: Transformation semigroups, idempotent generators, rank.II