consider the commutative diagram of group homomorphisms: $\begin{matrix} A&\stackrel{f}{\rightarrow}&B\\ \downarrow{g}&&\downarrow{k}\\ C&\stackrel{h}{\rightarrow}&D \end{matrix} $
suppose $B$, $C$ and $D$ are trivial groups $\{e\}$ does this imply that necessarely $A$ is also trivial?