Given $σ$ in $S_7$ where, $$σ=(14532)(67)$$ I know that this order of this element is $5$ as $σ^5=Id.$ I originally thought that the order of the element would be 10 as $lcm(5,2)=10$. Could someone please explain why this isn't the case?
2026-03-25 10:56:04.1774436164
Order of an element in Symmetric Group.
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Your theory is right, and your calculation is wrong. We have $$ \sigma^5 = (67) $$