For which n,n≥2, do the cycles in S_{n} form a subgroup? Do the odd permutations form a subgroup?
For it is true. Because any permutation is actually a cycle. But if then and are cyclic permutations while is not a cycle.
Correct. And the reason why it is not a subgroup is because a subgroup needs to be closed.Is the product of two odd permutations an odd permutation?
No. Therefore, the odd permutations does not form a subgroup.
Does my answer right?