C(G)一般指centralizer,
Z(G)表示center.
(假设你已经证明了center是G的子群)
if x belongs to Z(G) then xg=gx for all g in G
then gxg^-1 = g(xg^-1)=g(g^-1 x) = ex = x
true for all x in the center
hence g Z(G) g^-1 = Z(G)