Geodesic
Polygons with a (P, 1)-stable theory
Algebra i logika, Tome 56 (2017) no. 6, pp. 712-720

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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.
Keywords: $(P,1)$-stable theories
Mots-clés : polygons, $(P,1)$-stable polygons. 
@article{AL_2017_56_6_a4,
     author = {D. O. Ptakhov},
     title = {Polygons with a {(P,} 1)-stable theory},
     journal = {Algebra i logika},
     pages = {712--720},
     publisher = {mathdoc},
     volume = {56},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_6_a4/}
}
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D. O. Ptakhov. Polygons with a (P, 1)-stable theory. Algebra i logika, Tome 56 (2017) no. 6, pp. 712-720. http://geodesic.mathdoc.fr/item/AL_2017_56_6_a4/