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

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