ThmDex – An index of mathematical definitions, results, and conjectures.
Result R828 on D1629: Isomorphic groups
First group isomorphism theorem
Formulation 1
Let $G$ and $H$ each be a D22: Group such that
(i) $f : G \to H$ is a D948: Group homomorphism from $G$ to $H$
Then \begin{equation} G / \text{Ker}(f) \cong \text{Im}(f) \end{equation}