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).
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1044,
author = {Konrad Pi\'oro},
title = {On some finite groupoids with distributive subgroupoid lattices},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {22},
year = {2002},
pages = {25-31},
zbl = {1033.20076},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1044}
}
Konrad Pióro. On some finite groupoids with distributive subgroupoid lattices. Discussiones Mathematicae - General Algebra and Applications, Tome 22 (2002) pp. 25-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1044/
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