Let $f:G\to H$ be a group homomorphism. The kernel of $f$ is the collection of elements of $G$ that map to the indentity $e_H$ element of $H$. In set notation, we write $$\ker f = \{ g\in G\mid f(g)=e_H\}.$$

• I plan to introduce the kernel of a homorphism at the same time as introducing as introducing collapsible subgraphs. I plan to introduce this idea before introducing normal subgroups, and use the kernel to discover the definition of a normal subgroup.

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• http://en.wikipedia.org/wiki/Kernel_(algebra)#Group_homomorphisms

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