is a group. The operation on is defined by for all . Let be the map from G to itself such that where is the inverse of in group . Show that is a group isomorphism from to .
Attempt:
I think I have to show that is one to one, onto and it preserves order:
For "one to one":
For "onto":
I must find some such that .
So
And to show that it's operation preserving I did the following:
I appreciate it if anyone could correct any of my mistakes.