Much of the importance of quotient groups is derived from their relation to homomorphisms. The first isomorphism theorem states that the image of any group under a homomorphism is always isomorphic to a quotient of . Specifically, the image of under a homomorphism is isomorphic to where denotes the kernel of .
Much of the importance of quotient groups is derived from their relation to homomorphisms The first isomorphism theorem states that the image of any group under a homomorphism is always isomorphic to a quotient of  Specifically the image of under a homomorphism is isomorphic to where denotes the kernel of 