# Mappings, Homomorphisms and Subgroups

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Let @:G-->H be a homomorphism of G onto H, and let N be a normal subgroup of G. Show that @(N) is a normal subgroup of H.

How do I prove that a mapping is a normal subgroup of a group? What I am missing here is some understanding of the terminology and some clear understanding of mappings, homomorphisms, subgroups and normal subgroups. Please attempt to give me some understanding of what a problem like this is asking me. How can a mapping be a normal subgroup? What is a mapping from G-->H ? Is the mapping a set or group? Any help you can give would be great!

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Let F:G->H be a surjective group homomorphism, so ...

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