| Abstract | This is the first of a series of three papers involving bilateral semidirect product decompositions of monoids of transformations that preserve or reverse the order or the orientation on a finite set. In this paper we deal with the full transformation case. Namely, we consider the monoid $OR_n$ of all full transformations on a chain with $n$ elements that preserve or reverse the orientation, as well as its submonoids $OD_n$ of all order-preserving or order-reversing elements, $OP_n$ all orientation-preserving elements and $O_n$ of all order-preserving elements. |
