Transformation Semigroups Over Groups

conjugacy classes;wreath products;transformation semigroups

Petersen, Richard Francis ; Kailash Misra, Committee Member,Ronald Fulp, Committee Member,Tom Lada, Committee Member,Mohan S. Putcha, Committee Chair,Petersen, Richard Francis ; Kailash Misra ; Committee Member ; Ronald Fulp ; Committee Member ; Tom Lada ; Committee Member ; Mohan S. Putcha ; Committee Chair

University:North Carolina State University

关键词: conjugacy classes;    wreath products;    transformation semigroups;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/4128/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

The semigroup analogue of the symmetric group, S_{n}, is the full transformation semigroup, T_{n}. T_{n} is the set of all mappings from the set {1,2,..n} to itself. This semigroup has been studied in great detail, especially in connection with automata theory.The wreath product of a group G by S_{n} has been studied for almost one hundred years. In this thesis, we study the wreath product of a group G by T_{n}. These wreath products are expressed as GwrS_{n} and GwrT_{n}, respectively. Many interesting theorems and properties for wreath products will be discussed. For example, the result of John Howie that every element in T_{n} − S_{n} can be expressed as a product of idempotents, is generalized to show that any element of GwrT_{n}- GwrS_{n} can be expressed as a product of idempotents.It will also be shown that GwrT_{n} is unit regular.Chapter five begins with a review of Green's relations for a moniod, M. Green's relations for T_{n} are also reviewed and R and L-classes for the wreath product GwrT_{n} are determined. Finally, in the last two chapters, the conjugacy class structures of GwrT_{n} are determined. Just as the conjugacy classes of GwrS_{n} are indexed by colored partitions, we show that the conjugacy classes of GwrT_{n} are indexed by certain colored directed graphs.