# Groups and Integers

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

Â© BrainMass Inc. brainmass.com February 24, 2021, 2:20 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/groups-integers-14144

#### Solution Preview

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 ...

#### Solution Summary

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

$2.19