If σ Sn, show that σ2 = ε if and only if σ is a product of disjoint transpositions.
Added by Tyler L.
Step 1
If σ is a product of disjoint transpositions, then we can write σ as a composition of transpositions, where each transposition swaps two elements and does not affect any other elements. Let's say σ = (a1 a2)(a3 a4)...(an-1 an), where ai and ai+1 are swapped for Show more…
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