Kern (Gruppenhomomorphismus)

Let \(G,G'\) be groups, \(1 \in G'\) the neutral element and \(f: G \rightarrow G'\) a group homomorphism. Then the kernel is defined as

\begin{align*} \mathrm{ker}(f) \coloneqq \{g \in G \vert f(g) = 1\} \end{align*}