.Hello. Need some fast help on this:
Let G, \star)\rightarrow(H, \triangle) " alt="\phi G, \star)\rightarrow(H, \triangle) " /> be an isomorphism between these two groups. If is the inverse element of , then prove that is the inverse element of .
I tried like this:
Since is isomorphism, that means it is a one to one map thus
only when and since is isomorphism, must be the inverse of .
I can't see any explanation or justification here...in fact, the argument is true for ANY group homomorphism, isomorphism or not, and the proof is boringly simple:
Do you think my prove is enough, if not please elaborate.
Thanks for your time.