If I have the group $S_{9}$ and $\sigma, \tau \in S_{9}$ where $\vert \sigma \vert = 5$ and $\vert \tau \vert = 6$ is it then possible to have $\vert \sigma \tau \vert = 30$ and $\vert \sigma \tau \vert = 12$ why/why not?
Asked
Active
Viewed 66 times
1
-
3No element of $S_9$ has order $30$ (think about cycle types). – Chris Eagle Mar 31 '12 at 09:33
-
Not possible because $30\ne 12$... – lhf Apr 01 '12 at 02:59
-
1@lhf, I took it to be two separate questions, one about order 30, another about order 12. But, who knows? – Gerry Myerson Apr 01 '12 at 06:27
