The upper central series of a group G is the sequence of groups (each term normal in the term following it) 1 = Z_0<=Z_1<=Z_2<=...<=Z_n<=... that is constructed in the following way: 1.Z_1 is the center of G. 2. For n>1, Z_n is the unique subgroup of G such that Z_n/Z_(n - 1) is the center of G/Z_(n - 1). If the upper central series of a group terminates with Z_n = G for some n, then G is called a nilpotent group.