# Verbal subgroup of nilpotent group

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: verbal subgroup with a group property imposed on theambient group: nilpotent group

View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

## Contents

## Definition

A subgroup of a group is termed a **verbal subgroup of nilpotent group** if the whole group is a nilpotent group and the subgroup is a verbal subgroup.

## Relation with other properties

### Stronger properties

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

verbal subgroup of abelian group | |FULL LIST, MORE INFO |