\begin{definition}[Definition:Normal Series]
Let $G$ be a group whose identity is $e$.
A '''normal series''' for $G$ is a sequence of (normal) subgroups of $G$:
:$\set e = G_0 \lhd G_1 \lhd \cdots \lhd G_n = G$
where $G_{i - 1} \lhd G_i$ denotes that $G_{i - 1}$ is a proper normal subgroup of $G_i$.
\end{definition}