# Locally residually finite group

From Groupprops

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 propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Contents

## Definition

A group is termed **locally residually finite** if every finitely generated subgroup of the group is a residually finite group.

## Formalisms

### In terms of the locally operator

This property is obtained by applying the locally operator to the property: residually finite group

View other properties obtained by applying the locally operator

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Residually finite group | |FULL LIST, MORE INFO | |||

Locally finite group | |FULL LIST, MORE INFO | |||

Finite group | LERF group, Residually finite group|FULL LIST, MORE INFO |