Characteristically metacyclic group

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Definition

A group is termed characteristically metacyclic if it has a Cyclic characteristic subgroup (?) such that the quotient group is also a cyclic group.

Relation with other properties

Stronger properties

• Cyclic group
• Group with metacyclic derived series

Weaker properties

• Metacyclic group
• Polycyclic group
• Characteristically polycyclic group
• Supersolvable group

Facts

• Characteristically metacyclic and commutator-realizable implies abelian