Show that if H is any group and is an element of with , then there is a unique homomorphism from to such that --> .
Please help. Thank you.
define by it's obvious that is a homomorphism and you only need to prove that is basically well-defined:
if then for some integer thus: hence is well-defined. this proves the existence of such homomorphism.
now suppose is another homomorphism with then for all hence which proves the uniqueness.