Building on previous work in the nilspace-theoretic approach to the study of Host–Kra
factors of measure-preserving systems, we prove that every ergodic \mathbb{F}_{p}^{\omega}
F p ω -system of order k is a factor of an Abramov \mathbb{F}_{p}^{\omega} F p ω -system
of order k . This answers a question of Jamneshan, Shalom and Tao.
