Definition:Composition Series/Composition Factor

Theorem

Let $G$ be a group.

Let $\set e = G_0 \lhd G_1 \lhd \cdots \lhd G_{n - 1} \lhd G_n = G$ be a composition series for $G$.

Each of the quotient groups:

$G_1 / G_0, G_2 / G_1, \ldots, G_n / G_{n - 1}$

are the composition factors of $G$.

Sources

• 1978: John S. Rose: A Course on Group Theory ... (previous) ... (next): $1$: Introduction to Finite Group Theory: $1.9$