Characteristically polycyclic group

Definition
A group is termed characteristically polycyclic if there exists a characteristic series (i.e., a subgroup series where all the subgroups are characteristic) of finite length for the group, such that all the factor groups are cyclic groups.

Stronger properties

 * Weaker than::Cyclic group
 * Weaker than::Characteristically metacyclic group
 * Weaker than::Group with metacyclic derived series

Weaker properties

 * Stronger than::Supersolvable group
 * Stronger than::Polycyclic group

Facts

 * Automorphism group of characteristically polycyclic group is supersolvable