$\sigma = \pmatrix{1&2&3&4&5&6&7&8\\3 &8 &6 &7 &4 & 1 & 5 & 2} = (136)(28)(475)$
I just have a question about terminology. Would it be correct to say that $\sigma$ is not a cycle but $\sigma$ is a product of 3 disjoint cycles?
$\sigma = \pmatrix{1&2&3&4&5&6&7&8\\3 &8 &6 &7 &4 & 1 & 5 & 2} = (136)(28)(475)$
I just have a question about terminology. Would it be correct to say that $\sigma$ is not a cycle but $\sigma$ is a product of 3 disjoint cycles?
Yes it would be to correct to say that $\sigma$ is a product of $3$ disjoint cycles.