2.35 (1966)

An inverse spectrum $\xi$ of abelian groups is said to be acyclic if $\varprojlim^{(p)} \xi = 0$ for $p > 0$. Here $\varprojlim^{(p)}$ denotes the right derived functor of the projective limit functor. Let $\xi$ be an acyclic spectrum of finitely generated groups. Is the spectrum $\bigoplus \xi_\alpha$ also acyclic, where each spectrum $\xi_\alpha$ coincides with $\xi$?