A Note on Varieties of Groupoids Arising from <Emphasis Type="Italic">m</Emphasis>-Cycle Systems
نویسنده
چکیده
Decompositions of the complete graph with n vertices Kn into edge disjoint cycles of length m whose union is Kn are commonly called w-cycle systems. Any m-cycle system gives rise to a groupoid defined on the vertex set of Kn 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.
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Minimal bases for the laws of certain cycle systems
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