# Divisible normal subgroup

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): divisible group

View a complete list of such conjunctions

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

A subgroup of a group is termed a **divisible normal subgroup** if the subgroup is a divisible group and is also a normal subgroup of the whole group.

## Relation with other properties

### Weaker properties

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

local divisibility-closed subgroup | ||||

divisibility-closed subgroup |