Image and Kernel
We define the kernel of h to be the set of elements in G which are mapped to the identity in H
and the image of h to be
The kernel of h is a normal subgroup of G and the image of h is a subgroup of H:
The homomorphism h is injective (and called a group monomorphism) if and only if ker(h) = {eG}.
The kernel and image of a homomorphism can be interpreted as measuring how close it is to being an isomorphism. The First Isomorphism Theorem states that the image of a group homomorphism, h(G) is isomorphic to the quotient group G/ker h.
Read more about this topic: Group Homomorphism
Famous quotes containing the words image and/or kernel:
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—Blaise Pascal (16231662)
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—Anne Brontë (18201849)