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?
Permutation of order 12 and 30 in $S_{9}$
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$\begingroup$
permutations
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1@lhf, I took it to be two separate questions, one about order 30, another about order 12. But, who knows? – 2012-04-01
1 Answers
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$(12345)(234657)=(1365)(247)$.