# First isomorphism theorem

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Revision as of 15:19, 7 March 2008 by Vipul (talk | contribs) (New page: {{basic fact}} ==Statement== Let <math>G</math> be a group and <math>\varphi:G \to H</math> be a homomorphism of groups. The '''first isomorphism theorem''' states that the kerne...)

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This article gives the statement, and possibly proof, of a basic fact in group theory.

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## Statement

Let be a group and be a homomorphism of groups. The **first isomorphism theorem** states that the kernel of is a normal subgroup, say , and there is a natural isomorphism:

where denotes the image in of under .