# On the critical group of the missing Moore graph

@article{Ducey2017OnTC, title={On the critical group of the missing Moore graph}, author={Joshua E. Ducey}, journal={Discret. Math.}, year={2017}, volume={340}, pages={1104-1109} }

We consider the critical group of a hypothetical Moore graph of diameter $2$ and valency $57$. Determining this group is equivalent to finding the Smith normal form of the Laplacian matrix of such a graph. We show that all of the Sylow $p$-subgroups of the critical group must be elementary abelian with the exception of $p = 5$. We prove that the $5$-rank of the Laplacian matrix determines the critical group up to two possibilities.

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