Finitely generated solvable group

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

Definition

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

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finitely generated abelian group Finitely generated nilpotent group, Finitely presented solvable group, Polycyclic group, Supersolvable group|FULL LIST, MORE INFO
finitely generated nilpotent group Finitely presented solvable group, Polycyclic group, Supersolvable group|FULL LIST, MORE INFO
finite solvable group Finitely presented solvable group, Polycyclic group, Solvable group generated by finitely many periodic elements|FULL LIST, MORE INFO
polycyclic group solvable and every subgroup is finitely generated finitely generated and solvable not implies polycyclic Finitely presented solvable group|FULL LIST, MORE INFO
finitely presented solvable group solvable and has a finite presentation finitely generated and solvable not implies finitely presented |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finitely generated group |FULL LIST, MORE INFO
solvable group |FULL LIST, MORE INFO