Geodesic
A note on varieties of groupoids arising from $m$-cycle systems
Journal of Algebraic Combinatorics, Tome 4 (1995) no. 3, pp. 197-200.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Decompositions of the complete graph with $n$ vertices $K _{n}$ into edge disjoint cycles of length $m$ whose union is $K _{n}$ are commonly called $m$-cycle systems. Any $m$-cycle system gives rise to a groupoid defined on the vertex set of $K _{n}$ via a well known construction. Here, it is shown that the groupoids arising from all $m$-cycle systems are precisely the finite members of a variety (of groupoids) for $m = 3$ and 5 only.
Keywords: $m$-cycle system, variety, equationally denned, groupoid 
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     title = {A note on varieties of groupoids arising from $m$-cycle systems},
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Bryant, Darryn E. A note on varieties of groupoids arising from $m$-cycle systems. Journal of Algebraic Combinatorics, Tome 4 (1995) no. 3, pp. 197-200. http://geodesic.mathdoc.fr/item/JAC_1995__4_3_a3/