Upper central series
= Upper central series
{title2=$Z_0(G)=1,\quad Z_{i+1}(G)/Z_i(G)=Z(G/Z_i(G))$}
Repeatedly take the <center of a group> after quotienting by the preceding term. A <group> is a <nilpotent group> exactly when a finite term is the whole group. This yields the <normalizer condition for nilpotent groups>.