Normal series of a group

If $G$ is a {{KNOWL('group', 'group')}}, a **normal series** for $G$ is a chain of subgroups \[ \langle e\rangle =H_0 \lhd H_1 \lhd \cdots \lhd H_k=G\] where each {{KNOWL('group.subgroup', 'subgroup')}} is {{KNOWL('group.subgroup.normal','normal')}} in $G$.