Word Count : 248

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For (n\ge 5), consider the symmetric group (S_n) of all permutations of ({1,2,\dots ,n}) and its alternating subgroup (A_n) consisting of all even permutations. The index of (A_n) in (S_n) is 2, so the quotient group (S_n/A_n) has exactly two elements, ___ __________ ____ __________ ____ _________ _____ __________ _____ _____ ____ _____.
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