# Residually finite nilpotent group

From Groupprops

## Contents

## Definition

A **residually finite nilpotent group** is a group that is both a residually finite group and a nilpotent 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 propertiesVIEW 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: residually finite group and nilpotent 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 |
---|---|---|---|---|

residually finite abelian group | ||||

finite nilpotent group | ||||

conjugacy-separable nilpotent group |

### Weaker properties

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

residually finite solvable group |