Finitely presented solvable group
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 | |FULL LIST, MORE INFO | |||
| finitely generated abelian group | |FULL LIST, MORE INFO | |||
| finitely generated nilpotent 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 | |FULL LIST, MORE INFO | |||
| solvable group | |FULL LIST, MORE INFO |