Add a problem that asks students to explain why it is enough to verify that $g\in G$ is in center of $G$ by determining whether $g$ commutes with generators of $G$.
Probably should have a question like the following too: If $xg=gx$, then $xg^{-1}=g^{-1}x$. This should come before the problem above.
Add a problem that asks students to explain why it is enough to verify that $g\in G$ is in center of $G$ by determining whether $g$ commutes with generators of $G$.
Probably should have a question like the following too: If $xg=gx$, then $xg^{-1}=g^{-1}x$. This should come before the problem above.