Characteristically polycyclic group

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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.

Relation with other properties

Stronger properties

• Cyclic group
• Characteristically metacyclic group
• Group with polycyclic derived series

Weaker properties

• Supersolvable group
• Polycyclic group