First I am very confuse about the two term centralizer and center.
Second, how do I find centralizer of G when G= 1,2,3,4,5,6,7,8 and how do I find the center of G?
Thanks,
The center Z(G) is the set of all elements which commute with everything else. The centralizer C(x) of some element x in G is the set of all elements which commute with x.