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Groups and Integers

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Let m be the smallest positive integer such that @^m=E for all @eS_n. Show that m=lcm(2,3,4,5,...,n).

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Solution Summary

A proof involving groups and integers is provided. the proof is concise.

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E should mean 1 in S_n.
Proof: We know each permutation can be expressed as a product of some non-intersection cycles, where the length of the cycle is less than or equal to ...

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