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$\sigma = \pmatrix{1&2&3&4&5&6&7&8\\3 &8 &6 &7 &4 & 1 & 5 & 2} = (136)(28)(475)$

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?

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I believe your last cycle should be (475). Also, yes. – JSchlather Oct 26 '11 at 5:06
@JacobSchlather: Fixed and thanks for the quick response! – Student Oct 26 '11 at 5:07
@Jacob: Would you like to post an answer so the question can be listed as resolved? – Zev Chonoles Dec 25 '11 at 15:36
@ZevChonoles Done. – JSchlather Dec 26 '11 at 8:12
up vote 4 down vote accepted

Yes it would be to correct to say that $\sigma$ is a product of $3$ disjoint cycles.

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