# 1-completed subgroup

From Groupprops

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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

## Definition

### Symbol-free definition

A subgroup of a group is said to be **1-completed** if there is a single element outside the subgroup such that that element, along with the subgroup, generates the whole group.

### Definition with symbols

A subgroup of a group is said to be **1-completed** if there is an element in such that the subgroup generated by and is the whole of .

## Relation with other properties

### Stronger properties

### Weaker properties

## Metaproperties

### Upward-closedness

This subgroup property is upward-closed: if a subgroup satisfies the property in the whole group, every intermediate subgroup also satisfies the property in the whole group

View other upward-closed subgroup properties