Composition series

Definition
A composition series for a group is a subnormal series where all the quotient groups (of successive terms) are simple groups.

Weaker properties

 * Stronger than::Subnormal series

Incomparable properties

 * Chief series

Facts

 * If a group has two composition series, then they both have the same length, and each simple group occurs with the same multiplicity as a quotient in both. This is the content of the Jordan-Holder theorem.