Problem:
Suppose R is a ring, G, M are R-modules and Hom(G,M) is the set of R-module homomorphisms from G to M.
Identify Hom(Z/nZ,Z), Hom(Z,Z/nZ), Hom(Z/3Z,Z/6Z), Hom(Z/10Z,Z/6Z) as abelian groups, where n belongs to Z and Z is the set of integers.
Provide complete and step by step solution for the question and show calculations and use formulas.