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Groupprops β

Composition series

This article defines a property that can be evaluated for a subgroup series

View a complete list of properties of subgroup series



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


  • 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.