Characteristically metacylic group

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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
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

Definition

A group G is termed characteristically metacyclic if there exists a characteristic subgroup H of G such that both H and the quotient group (note that characteristic implies normal, so the quotient group does exist) G/H are cyclic groups.

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
metacyclic group
characteristically polycyclic group |FULL LIST, MORE INFO
polycyclic group (via metacyclic) (via metacyclic) Characteristically polycyclic group|FULL LIST, MORE INFO
supersolvable group (via metacyclic) (via metacyclic) Characteristically polycyclic group|FULL LIST, MORE INFO
solvable group (via metacyclic) (via metacyclic) |FULL LIST, MORE INFO