Finitely presented residually finite group

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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
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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 Finitely presented conjugacy-separable group|FULL LIST, MORE INFO
finitely generated free group Finitely presented conjugacy-separable 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 Finitely generated residually finite group|FULL LIST, MORE INFO
finitely generated Hopfian group