Most subrings of ${\mathbb{Z}}^n$ have large corank

Gautam Chinta, Kelly Isham, Nathan Kaplan

If $\Lambda \subseteq {\mathbb{Z}}^n$ is a sublattice of index $m$, then ${\mathbb{Z}}^n/\Lambda$ is a finite abelian group of order $m$ and rank at most $n$. Several authors have studied statistic…