Alternating Group A3 is a Normal Subgroup

is a subgroup of in which all the cycles in the set are even permutations. Since every has terms and half of them are even and half of them are odd. In we have terms. Therefore in we have half of 6 or 3 terms. One of the reason we are interested in alternating group is because they form Normal subgroups i.e left coset and right coset are same.