The third isomorphism theorem states that for a given group, if you have a normal subgroup and a quotient group, the quotient of the quotient group by the image of the normal subgroup is isomorphic to the quotient of the original group by the normal subgroup. This theorem highlights how the structure of groups can be understood through their subgroups and quotient groups, and it's an important tool for analyzing homomorphisms and group structures in algebra.
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