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first isomorphism theorem

Mar 19, 20252 min read

first isomorphism theorem

This theorem is extremely useful for identifying/ understanding groups by using a homomorphism from a known/ understood group.

Theorem

Let be a group homomorphism.

  1. is a subgroup
  2. is a normal subgroup

Special case (surjective)

Let be a surjective group homomorphism. Then .

Picture:

Proof

todo

References

Graph View

first isomorphism theoremgroupsimple field extensionexterior poweraffine algebraic varietyMarsden-Weinstein symplectic reduction theorem

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