Let
G be a finite group and H a subgroup of G. Let a be an element of G
and aH = {ah : h is an element of H} be a left coset of H. If b is
an element of G as well and the intersection of aH bH is non-empty
then aH and bH contain the same number of elements in G. Thus
conclude that the number of elements in H, o(H), divides the number
of elements...