Spectral Tile Direction in the Group ${\mathbb{Z}}_{p^2}\times {\mathbb{Z}}_{q^2}\times {\mathbb{Z}}_r$

Thomas Fallon, Gergely Kiss, Azita Mayeli +1

Let $p$, $q$, and $r$ be distinct primes such that $p^2{q}^2<r$. We prove that every spectral set in the cyclic group ${\mathbb{Z}}_{p^2{q}^{2}r}$ is a tile. Since the reverse direction is…