Question

Let G = Z₁₂ x Z₁₈: N = (([6]₁₂, [12]₁₈)), g = ([3]₁₂, [2]₁₈)

a. Find N and G/N, and write the elements of N.
b. Find the order of g in G and find the order of gN in the quotient group G/N.
c. Show that h¹⁸ ∈ N for all he G.
d. Show the quotient group G/N is not cyclic.