Fuglede’s conjecture holds on ℤ_{

The study of Fuglede’s conjecture on the direct product elementary abelian groups was initiated by Iosevich et al. For two holds. Z p 3 \mathbb {Z}_p^3 problem is still open if alttext="p"> encoding="application/x-tex">p prime and alttext="p greater-than-or-equal-to 11"> ≥ 11 encoding="application/x-tex">p\ge 11 . In connection we prove that holds 2 Baseline times double-struck q"> 2 ×<!-- × <mml:msub> q {Z}_{p}^2\times \mathbb {Z}_q developing a method based ideas from discrete geometry.