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====== Group Homomorphism ======
====Definition==== 
Let $(G,\cdot)$ and $(H,\times)$ be [[definition:group|groups]]. We say that the function $f:G\to H$ is a group $\textdef{homomorphism}$ if $f(a\cdot b)=f(a)\times f(b)$ for every $a,b\in G$.


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==== Remarks ==== 
  * I would like to add something along the lines of "The map is compatible with the group structures of both $G$ and $H$" to the definition above.  If someone has a good way of stating this, feel free to add it above.


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==== $\LaTeX$ version ====
<code>
%%%%%
% DEPENDENCIES 
% RequiredMacros: \DeclareMathOperator{\syl}{Syl} 
%%%%%
\begin{definition}
Type the definition using LaTeX syntax.
\end{definition}
</code>

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==== External links ====
  * [[wp>Group homomorphism]]


{{tag>definition ben needsreview rben rjosh}}

Abstract Algebra IBL Wiki

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