6.36 (1978)

(J. W. Grossman). The nilpotent-completion diagram of a group $G$ is as follows: $G/\gamma_1G \leftarrow G/\gamma_2G \leftarrow \dots$, where $\gamma_iG$ is the $i$th term of the lower central series and the arrows are natural homomorphisms. It is easy to see that every nilpotent-completion diagram $G_1 \leftarrow G_2 \leftarrow \dots$ is a $\gamma$-diagram, that is, every sequence $1 \to \gamma_s G_{s+1} \to G_{s+1} \to G_s \to 1$, $s = 1, 2, \dots$, is exact. Do $\gamma$-diagrams exist that are not nilpotent-completion diagrams?