Alternating Group

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 $n$.

• See 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 symmetric group $S_n$, with order $n!/2$.

alternating_group.tex

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\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}

• Alternating group

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