The first problem (10.5.1) in Dummit&Foote about Exact Sequences is a diagram chase. We're given a commutative diagram of groups with exact rows $$\require{AMScd} \begin{CD} A @>{\psi}>> B @>{\varphi}>> C\\ @V{\alpha}VV @V{\beta}VV @V{\gamma}VV\\ A' @>{\psi'}>> B' @>{\varphi'}>> C' \end{CD} $$ Part (d) of the problem requires the reader to prove: If $\beta$ is injective and $\alpha, \gamma$ are surjective, then $\gamma$ is injective.
All of the other parts weren't too difficult but I struggle on this one. I eventually checked the errata. There he said that this part was wrong in the 2nd edition (I have the 3rd) and it changed "$\beta$ injective, $\alpha, \gamma$ surjective " to "$\beta$ injective, $\alpha, \varphi$ surjective".
That's a little weird though because the "corrected version" is not what is written in the book. To top it off, that would be exactly part (a).
So does anybody know what the problem should really be? (I know that the initial version is wrong because I have just constructed a counterexample... However it's weird that the correction of (d) would coincide with (a) but perhaps that's just a small error in the book.)