Let G be a group, and let a E G.  Prove that C(a) = C(a-1).

If f: Z -> Z is the map defined by f(x) = 2x. Is f a group homomorphism when the group operation on Z is addition? How would you prove it?

a.) Explain in your own words what this problem is asking. b.) Explain the meaning of any notation used in the problem and in your solution. c.) Describe the mathematical concept(s) that appear to be foundational to this problem. d.) Justified solution to or proof of the problem.

22. The center Z(G) of a group G is defined as Z(G) = = {a Є G|ax = xa for all x Є G}.