= Isomorphism theorems
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The <isomorphism theorems> relate <homomorphisms>, their kernels and images, and quotient constructions in <algebra>. For <groups>, the <first isomorphism theorem> identifies a homomorphism's image with the <quotient group> by its <group kernel>. Analogous statements include the <first isomorphism theorem for rings> and the <First isomorphism theorem for vector spaces>: identifying precisely the inputs with the same output preserves the remaining algebraic structure.
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