Let such that where . Since is a group homomorphism we see that . On the other hand . Therefore, .
Allright here is a problem from one of my hw assignments and i have no idea how to solve it. Im sure there is probably a theorem or something that can be used to make it quite easy but i cant think of anything.
Let F: G->G' be a group homomorphism and suppose a is in G and a has finite order. Prove that the ord(F(a)) divides ord(a)