Composition factor-unique group

Symbol-free definition
A group is said to be composition factor-unique if the order in which its composition factors occur is the same for every composition series.

Stronger properties

 * Weaker than::Characteristically simple group
 * Weaker than::Group of prime power order
 * Weaker than::Composition series-unique group

Weaker properties

 * Stronger than::Group of finite composition length: For a proof that the order of composition factors need not be the same for all composition series, refer finite not implies composition factor-unique.