Polygons with a (P, 1)-Stable Theory

详细

Polygons with a (P, 1)-stable theory are considered. A criterion of being (P, 1)-stable for a polygon is established. As a consequence of the main criterion we prove that a polygon _SS, where S is a group, is (P, 1)-stable if and only if S is a finite group. It is shown that the class of all polygons with monoid S is (P, 1)-stable only if S is a one-element monoid. (P, 1)-stability criteria are presented for polygons over right and left zero monoids.