====== Alternating Group ======
====Definition==== 
The $\textdef{alternating group}$ of degree $n$, or alternating group on $n$ letters, is the [[definition:permutation group]] of [[definition:even permutation]]s on $n$ elements. We'll use the notation $A_n$ to denote the alternating group of degree $n$.  


----
==== Remarks ==== 
  * See [[problem:soccerballahedron]] to contruct the Cayley graph on $A_5$.
  * We should have a problem (probably really easy) that has the students prove that $A_n$ is a subgroup of the [[definition:symmetric group]] $S_n$, with order $n!/2$. 


----
==== $\LaTeX$ version ====
<file tex alternating_group.tex>
%%%%%
% DEPENDENCIES 
% RequiredMacros: \newcommand{\textdef}[1]{\textit{#1}}
%%%%%
\begin{definition}
The $\textdef{alternating group}$ of degree $n$, or alternating group on $n$ letters, is the permutation group of even permutations on $n$ elements. We'll use the notation $A_n$ to denote the alternating group of degree $n$.
\end{definition}
</file>

----
==== External links ====
  * [[wp>Alternating group]]


{{tag>definition ben needsreview rben rdana rjosh complete}}