Prove that every finite group $G$ is isomorphic to a group of even permutations.
Let $G$ be a finite group . By Cayley's Theorem $G$ is isomorphic to a subgroup of $S_n$. Let $\tau $ be the required isomorphism under which $g\mapsto \tau(g)$.
If $\tau(g)$ is even we are done.If not we will have to turn $\tau(g)$ into an even permutation which I am failing to do.
Please help on how should I proceed.