The next theorem tells us that under a homomorphism, the order of the image of an element must divide the order of the pre-image of that element. The next theorem tells us that two elements in the dom...The next theorem tells us that under a homomorphism, the order of the image of an element must divide the order of the pre-image of that element. The next theorem tells us that two elements in the domain of a group homomorphism map to the same element in the codomain if and only if they are in the same coset of the kernel.
