Geodesic
Interassociativity and three-element doppelsemigroups
Algebra and discrete mathematics, Tome 28 (2019) no. 2, pp. 224-247

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In the paper we characterize all interassociates of some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism groups. We prove that there exist $75$ pairwise non-isomorphic three-element doppelsemigroups among which $41$ doppelsemigroups are commutative. Non-commutative doppelsemigroups are divided into $17$ pairs of dual doppelsemigroups. Also up to isomorphism there are $65$ strong doppelsemigroups of order $3$, and all non-strong doppelsemigroups are not commutative.
Keywords: semigroup, interassociativity, doppelsemigroup, strong doppelsemigroup. 
@article{ADM_2019_28_2_a7,
     author = {Volodymyr Gavrylkiv and Diana Rendziak},
     title = {Interassociativity and three-element doppelsemigroups},
     journal = {Algebra and discrete mathematics},
     pages = {224--247},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_28_2_a7/}
}
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Volodymyr Gavrylkiv; Diana Rendziak. Interassociativity and three-element doppelsemigroups. Algebra and discrete mathematics, Tome 28 (2019) no. 2, pp. 224-247. http://geodesic.mathdoc.fr/item/ADM_2019_28_2_a7/