Group with metacyclic derived series
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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
Contents
Definition
A group with metacyclic derived series is a group with the property that its commutator subgroup as well as abelianization are both cyclic groups.
Relation with other properties
Stronger properties
Weaker properties
- Characteristically metacyclic group: For proof of the implication, refer metacyclic derived series implies characteristically metacyclic and for proof of its strictness (i.e. the reverse implication being false) refer Characteristically metacyclic not implies metacyclic derived series.
- Metacyclic group
