Three subgroup common transversal in abelian groups

Abstract

We completely characterize when three equal-order subgroups of a finite abelian group share a common transversal. Consequently, we determine when three full-rank lattices of equal volume with a discrete sum in ${\mathbb{R}}^d$ admit a common fundamental domain, answering, for $n=3$, an open question from 1997.

28 pages