1. The problem statement, all variables and given/known data Show that for every subgroup H of S(n) [the symmetric group on n letters] for n>=2 either all the permutations in H are even or exactly half of them are even. 2. Relevant equations 3. The attempt at a solution I didn't really know how to do this but i thought maybe since H is closed it has something to do with the fact that an odd permutation times an odd permutation produces an even permutation and an odd permutation times an even permutation produces an odd permutation.