Finitely presented residually finite group
Definition
A finitely presented residually finite group is a group that is both finitely presented and residually finite.
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 residually finite 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 |
|---|---|---|---|---|
| finitely presented conjugacy-separable group | |FULL LIST, MORE INFO | |||
| finitely generated abelian group | |FULL LIST, MORE INFO | |||
| finitely generated free group | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| group with solvable word problem | finitely presented and residually finite implies solvable word problem | |FULL LIST, MORE INFO | ||
| finitely generated residually finite group | finitely presented implies finitely generated | |FULL LIST, MORE INFO | ||
| Hopfian group | via finitely generated residually finite | |FULL LIST, MORE INFO | ||
| finitely generated Hopfian group |