Complete graph decompositions and p-groupoids
Group Theory
2019-04-11 v1 Combinatorics
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.
Cite
@article{arxiv.1904.04856,
title = {Complete graph decompositions and p-groupoids},
author = {John Carr and Mark Greer},
journal= {arXiv preprint arXiv:1904.04856},
year = {2019}
}