Composition series
From Groupprops
This article defines a property that can be evaluated for a subgroup seriesView a complete list of properties of subgroup series
Contents
Definition
A composition series for a group is a subnormal series where all the quotient groups (of successive terms) are simple groups.
Relation with other properties
Weaker properties
Incomparable properties
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.
