Let G be a simply connected simple Lie group and C the center of G, which is isomorphic with the fundamental group of the adjoint group of G. For an element c of C, an element x of the Lie algebra g of G is called a representative of c in g if exp x = c. Sirota-Solodovnikov [7] found a complete set of representatives of the center C in g and studied the group structure of C, and using their results Goto-Kobayashi [1] classified subgroups of the center C with respect to automorphisms of G. The group structure of C was also studied in Takeuchi [8],