Geodesic
On some finite groupoids with distributive subgroupoid lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 1, pp. 25-31

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The aim of the paper is to show that if S(G) is distributive, and also G satisfies some additional condition, then the union of any two subgroupoids of G is also a subgroupoid (intuitively, G has to be in some sense a unary algebra).
Keywords: groupoid, subgroupoid lattice, distributive lattice 
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Pióro, Konrad. On some finite groupoids with distributive subgroupoid lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 1, pp. 25-31. http://geodesic.mathdoc.fr/item/DMGAA_2002_22_1_a1/