Let m be the smallest positive integer such that @^m=E for all @eS_n. Show that m=lcm(2,3,4,5,...,n).
note: e denotes element of
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 ...
A proof involving groups and integers is provided. the proof is concise.