First group isomorphism theorem

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Note:

• Overview of the group isomorphism theorems - all 3 theorems in one place
• Overview of the isomorphism theorems - the first, second and third are pretty much the same just differing by what objects they apply to

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
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Statement

First group isomorphism theorem\Statement