2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72168It will be shown that if $ϕ$ is a quasiperiodic flow on the $n$-torus that is algebraic, if $ψ$ is a flow on the $n$-torus that is smoothly conjugate to a flow generated by a constant vector field, and if $ϕ$ is smoothly semiconjugate to $ψ$, then $ψ$ is a quasiperiodic flow that is algebraic, and the multiplier group of $ψ$ is a finite index subgroup of the multiplier group of $ϕ$. This will partially establish a conjecture that asserts that a quasiperiodic flow on the $n$-torus is algebraic if and only if its multiplier group is a finite index subgroup of the group of units of the ring of integers in a real algebraic number field of degree $n$.Submitted to the Proceedings of the AIMS' Fifth International Conference on Dynamical Systems and Differential EquationsDynamical SystemsGroup Theory37C55; 37C80; 20E34; 11R04text