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


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==== Remarks ==== 
  * I plan to introduce the kernel of a homorphism at the same time as introducing as introducing [[definition:collapsible subgraph]]s.  I plan to introduce this idea before introducing [[definition:normal subgroup]]s, and use the kernel to discover the definition of a normal subgroup. 


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==== $\LaTeX$ version ====
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==== External links ====
  * [[wp>Kernel_(algebra)#Group_homomorphisms]]


{{tag>definition ben needsreview rben}}

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