Group whose chief series are composition series

Definition
A group whose chief series are composition series is a group that satisfies the following equivalent conditions:


 * 1) The group has finite composition length, and finite chief length, and the two lengths are equal.
 * 2) The group has a defining ingredient::chief series of finite length that is also a defining ingredient::composition series.
 * 3) The group has a chief series of finite length, and every chief series for the group is a composition series.

Note that it is not necessary for such a group that every composition series is a chief series. In fact, every composition series is a chief series if and only if the group is a T-group having finite composition length, i.e., it has finite composition length, and every subnormal subgroup is normal. This is because any subnormal series can be refined to a composition series for a group of finite composition length.

Stronger properties

 * Weaker than::Simple group
 * Weaker than::Group of composition length two
 * Weaker than::Finite nilpotent group
 * Weaker than::Finite supersolvable group

Weaker properties

 * Stronger than::Group of finite chief length
 * Stronger than::Group of finite composition length