Lifting Primitivity of Free Nilpotent Groups
Gupta Rk, Narain Gupta · Proceedings of the American Mathematical Society · 1992
Let ${F_{n,c}}$ denote the free $n$-generator nilpotent group of class $c$. For $n \geq c + m - 1$, every primitive system of $m$ elements of ${F_{n,c}}$ can be lifted to a primitive system of $m$ elements of the free group ${F_n}$.