3. Let On be the set of odd permutations in Sn. Is On a subgroup? Solution No, On is not a subgroup.. to see that the odd permutations don\'t form a subgroup of Sn is a bit easier to resolve. Recall that any subgroup of Sn has the same identity element as the identity element in Sn. But since the identity element in Sn is not an odd permutation (a result we saw in class), it follows that the collection of odd permutations cannot be a subgroup of Sn. (One could also argue that the odd elements aren\'t closed under the group operation.).