For a $k$-uniform hypergraph $\mathcal{ H}$ on vertex set $\{ 1, ..., n\}$ we associate a particular signed incidence matrix $M(\mathcal{ H})$ over the integers. For $\mathcal{ H} \sim \mathcal{ H}_k(n, p)$ an Erd\H{ o}s--R\'{ e}nyi random $k$-uniform hypergraph, $\text{ coker}(M(\mathcal{ H}))$ is then a model for random abelian groups. Motivated by conjectures from the study of random simplicial complexes we show that for $p = \omega(1/n^{ k - 1})$, $\text{ coker}(M(\mathcal{ H}))$ is torsion-free.
Categories: math.CO math.PR