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. 
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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/

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