Locally maximal regular subsemibands of \(\mathcal{SOP}_n\). (Q400811)

The main result of this paper gives a classification for all locally maximal regular subsemibands in the semigroup of all singular orientation preserving transformations of a finite cycle. It turns out that there are two classes of such subsemibands, both indexed by an element \(i\) of the cycle. The corresponding semigroup in the first class consists of all transformations fixing \(i\). The corresponding semigroup in the second class consists of all order preserving transformations of the chain which is obtained by breaking the cycle at \(i\).