Is there a theorem or any useful application for knowing the order of a permutation belonging to the symmetric group Sn?(adsbygoogle = window.adsbygoogle || []).push({});

For example,

Lets say σ is a permutation belonging to S5; i.e. σ is a permutation of {1,2,3,4,5}. If we are given that σ^7 = I (the identity permutation), then how can we show that necessarily σ = I ?

Thank you all for your time and help.

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# Basic Question: Order of permutations in Sn

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