# Permutations : Disjoint Transpositions

If $ belongs to Sn (where Sn is the symmetric group of degree n), show that $^2 = % if and only if $ is a product of disjoint transpositions.

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#### Solution Preview

Here % should mean the unit 1.

If $ is a product of disjoint transpositions, then $=a1*a2...*ak, where ai are ...

#### Solution Summary

A proof involving symmetric groups and disjoint transpositions is provided. The proof is concise.

$2.19