Group of finite chief length

Definition
A group of finite chief length is a group satisfying the following equivalent conditions:


 * It possesses a defining ingredient::chief series of finite length, i.e., a defining ingredient::normal series of finite length that cannot be further refined.
 * It satisfies the ascending chain condition on normal subgroups as well as the descending chain condition on normal subgroups.

Stronger properties

 * Weaker than::Finite group
 * Weaker than::Simple group
 * Weaker than::Group of finite composition length

Weaker properties

 * Stronger than::Group satisfying ascending chain condition on normal subgroups
 * Stronger than::Group satisfying descending chain condition on normal subgroups