Let H be a normal subgroup of G and a ∈ G such that o(a) = n (i.e. the order of a is n).

(a) Show that S = {k ∈ N |ak ∈ H} is not empty.

(b) Show that S has the minimum element say m, and m is the order of an element aH of G/H.

(c) Prove that m divides n.