Group in which every subgroup is finitely presented

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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
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Definition

A group in which every subgroup is finitely presented is defined as a group in which every subgroup is a finitely presented group.

Formalisms

In terms of the hereditarily operator

This property is obtained by applying the hereditarily operator to the property: finitely presented group
View other properties obtained by applying the hereditarily operator

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finitely generated abelian group both finitely generated and abelian Finitely generated nilpotent group|FULL LIST, MORE INFO
Finitely generated nilpotent group both finitely generated and nilpotent |FULL LIST, MORE INFO
Polycyclic group has a subnormal series where all the successive quotients are cyclic groups |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Noetherian group every subgroup is finitely generated |FULL LIST, MORE INFO
Finitely presented group has a finite presentation |FULL LIST, MORE INFO
Finitely generated group |FULL LIST, MORE INFO