5.9 (1976)

Let $1 \to R_i \xrightarrow{\pi_i} F \to G \to 1$, $i = 1, 2$, be two exact sequences of groups with $G$ finite and $F$ free of finite rank $d(F)$. If we assume that $d(F) = d(G) + 1$ (where $d(G)$ is the minimum number of generators of $G$), are the corresponding abelianized extensions isomorphic?