Show that every odd permutation in S_n is a product of σ and some permutation in A_n?
consider S_n for a fixed n ≥ 2 and let σ be a fixed odd permutation. Show that every odd permutation in S_n is a product of σ and some permutation in A_n
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If g is another odd permutation, then g σ^{-1} is an even permutation.