structural:scholar_edition, structural:expansion
Example

Let G be the cyclic group on 6 elements {0, 1, 2, 3, 4, 5} with modular addition, H be the cyclic on 2 elements {0, 1} with modular addition, and f the homomorphism that maps each element g in G to the element g modulo 2 in H. Then ker f = {0, 2, 4}, since all these elements are mapped to 0. The quotient group G / (ker f) has two elements: {0, 2, 4} and {1, 3, 5}. It is indeed isomorphic to H.