Solution
= Solution
{c}
Suppose $\sigma$ has <order of a group element> two. On a cycle of length $k$, $\sigma^2$ moves each entry two places. Since $\sigma^2=e$, every such $k$ divides two, so $k=1$ or $k=2$. After omitting the fixed points, the <disjoint cycle decomposition> is therefore a product of <disjoint permutation cycles> of length two, which are <transpositions>. There is at least one, because $\sigma\ne e$.