20M20 05A10 05A15 20M18 (left) waist of \(\alpha\) (partial) derangement 20M17 breadth collapse fix fix of \(\alpha\) full transformation height height and right (left) waist of a transformation. Idempotents and nilpotents height of \(\alpha\) orthodox semigroups partial one-one transformation partial one-to-one transformation partial transformation permutation quasi-adequate semigroups regularity right (left) waist and fix of a transformation. Idempotents and nilpotents starred Green's relations symmetric inverse monoid