Definition:Normal Series/Factor Group

Definition
Let $G$ be a group whose identity is $e$. Let $\left \langle {G_i}\right \rangle_{i \in \left[{0 \,.\,.\, n}\right]}$ be a normal series for $G$:
 * $\left \langle {G_i}\right \rangle_{i \in \left[{0 \,.\,.\, n}\right]} = \left({\left\{{e}\right\} = G_0 \lhd G_1 \lhd \cdots \lhd G_{n-1} \lhd G_n = G}\right)$

The factor groups of $\left \langle {G_i}\right \rangle_{i \in \left[{0 \,.\,.\, n}\right]}$:
 * $\left\{{e}\right\} = G_0 \lhd G_1 \lhd \cdots \lhd G_n = G$

are the quotient groups:
 * $G_1 / G_0, G_2 / G_1, \ldots, G_i / G_{i-1}, \ldots, G_n / G_{n-1}$

Also known as
A factor group is also referred to as a factor.