(1) Prove that for any finitely generated abelian group G, the set Hom(G, Z) is a free Abelian group of finite rank.
(2) Find the rank of Hom(G,Z) if the group G is generated by three generators x, y, z with relations 2x + 3y + z = 0, 2y - z = 0
(1) Prove that for any finitely generated abelian group G, the set Hom(G, Z) is a free Abelian group of finite rank.
(2) Find the rank of Hom(G,Z) if the group G is generated by three generators x, y, z with relations 2x + 3y + z = 0, 2y - z = 0