J. Jezek, Department of Algebra, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic, e-mail: jezek@karlin.mff.cuni.cz
Abstract: Slim groupoids are groupoids satisfying $x(yz)xz$. We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such groupoids are inherently nonfinitely based) and find all strongly nonfinitely based slim groupoids with at most four elements; up to isomorphism, there are just two such groupoids.
Keywords: groupoid, variety, nonfinitely based
Classification (MSC 2000): 20N02
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