Characteristically polycyclic group

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Contents

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 metacyclic derived series

Weaker properties

• Supersolvable group
• Polycyclic group

Facts

• Automorphism group of characteristically polycyclic group is supersolvable

References

Journal references

• Groups with a characteristic cyclic series by John R. Durbin and Merry McDonald, Journal of Algebra, ISSN 00218693, Volume 18, Page 453 - 460(Year 1971): ^{PDF (ScienceDirect)More info}