The notion of topological predictability was introduced by Kamiński, Siemaszko and Szymański in 2003. A topological dynamical system $(X,T)$ is said to be topologically predictable if every continuous function on $X$ belongs to the closed algebra generated by $1,Tf,T^2f,T^3f,\ldots$. Kamiński, Siemaszko and Szymański showed in 2005 that topologically predictable systems have zero topological entropy. In 2012, Hochman extended this result to $\mathbb{Z}^d$-actions, and asked if it also holds for amenable group actions. In this talk, we partially answer this question affirmatively for actions of torsion-free nilpotent groups. A key tool is an algebraic theorem due to Rhemtulla and Formanek. We will give an independent proof of the Rhemtulla-Formanek theorem for torsion-free abelian groups and the Heisenberg group. This is a joint work with Huang and Ye.