Finitely presented solvable group

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Definition

A finitely presented solvable group is a group that is both a finitely presented group and a solvable group.

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
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: finitely presented group and solvable group
View other group property conjunctions OR view all group properties

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finite solvable group Polycyclic group|FULL LIST, MORE INFO
finitely generated abelian group Polycyclic group|FULL LIST, MORE INFO
finitely generated nilpotent group Polycyclic group|FULL LIST, MORE INFO
polycyclic group solvable and every subgroup is finitely generated polycyclic implies finitely presented finitely presented and solvable not implies polycyclic |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finitely generated solvable group finitely presented implies finitely generated finitely generated and solvable not implies finitely presented |FULL LIST, MORE INFO
finitely presented group |FULL LIST, MORE INFO
finitely generated group Finitely generated solvable group|FULL LIST, MORE INFO
solvable group Finitely generated solvable group|FULL LIST, MORE INFO