Subsemigroup structure of finite transformation semigroups.
James Charles Higgins · Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School) · 1970
Both necessary conditions and sufficient conditions in order that a subset of a finite transformation semigroup be a subsemigroup are developed in this paper. The existence of several subsemigroups of various orders is established. Also, some results concerning idem- potents and generators of idempotents are proved. Then certain classes of subsemigroups are defined according to their idempotent structure and isomorphisms are demonstrated between these classes. Examples from the transformation semigroup on three elements are supplied throughout the paper.