Please can you help me with this question:
Define the following map on a cyclic finite group G:
f:G--> G x|-->f(x):=x^m
where m is a fixed interger prove f is a group morphism and establish one condition whether sufficent of necessary for f to be a monomorphism.
I know that x^m is a cyclic group
I also know a monomorphism is an injective homomorphism, which is one to one as a function which relates maybe to f:G-->G.
When it asks to prove it is a group morphism does this mean I need to find the kernal and the image.
I know what the question means but just don't know the proof of it.
Any help would be great thanks