First group isomorphism theorem

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Note:
First isomorphism theorem
[ilmath]\begin{xy}\xymatrix{A \ar[r]^\varphi \ar[d]_{\pi} & B \\ A/\text{Ker}(\varphi) \ar@{.>}[r]^-{\theta}& \text{Im}(\varphi) \ar@{^{(}->}[u]^i }\end{xy}[/ilmath]
Where [ilmath]\theta[/ilmath] is an isomorphism.
Properties
something

Statement

First group isomorphism theorem\Statement

Proof

Notes

References