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# Permutations : Disjoint Transpositions

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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.

##### Solution Summary

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

##### Solution Preview

Here % should mean the unit 1.

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

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