Assignment:
Let G be a group and S any subset of G. Prove that C_G (S) = {g in G such that gs = sg for all s in S} is a subgroup of G. Prove that Z (G) (center of G) = C_G (S) is abelian and is a normal subgroup of G.
Provide complete and step by step solution for the question and show calculations and use formulas.