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arXiv · 1904.04856

Complete graph decompositions and p-groupoids

John Carr·Mark Greer
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Abstract

We study P-groupoids that arise from certain decompositions of complete graphs. We show that left distributive P-groupoids are distributive, quasigroups. We characterize P-groupoids when the corresponding decomposition is a Hamiltonian decomposition for complete graphs of odd, prime order. We also study a specific example of a P-quasigroup constructed from cyclic groups of odd order. We show such P-quasigroups have characteristic left and right multiplication groups, as well as the right multiplication group is isomorphic to the dihedral group.

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John Carr, Mark Greer. 2019-04-09. Complete graph decompositions and p-groupoids. https://arxiv.org/abs/1904.04856

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