Category:Composition Series

This category contains results about Composition Series.
Definitions specific to this category can be found in Definitions/Composition Series.

Let $G$ be a finite group.

Definition 1

A composition series for $G$ is a normal series for $G$ which has no proper refinement.

Definition 2

A composition 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 $G_i$

such that:

for all $i \in \set {1, 2, \ldots, n}$, $G_{i - 1}$ is a proper maximal normal subgroup of $G_i$.