# Trivial subgroup

From Groupprops

(Redirected from Trivial property)

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]

## Definition

A subgroup of a group is said to be the **trivial subgroup** or satisfy the *trivial property* if and only if it is the trivial group (viz the group with one element, the identity element).

## Relation with other properties

### Related metaproperties

- Trivially true subgroup property is the subgroup metaproperty of being weaker than the trivial property. In other words, a subgroup property is said to be trivially true if it is always satisfied by trivial subgroups.