# Trivially true subgroup property

From Groupprops

This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property

View a complete list of subgroup metaproperties

View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metapropertyVIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

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

This article is about a general term. A list of important particular cases (instances) is available at Category: Trivially true subgroup properties

## Definition

### Symbol-free definition

A subgroup property is said to be **trivially true** if, in any group, the trivial subgroup (that is, the subgroup comprising only the identity element) satisfies the property.

## Relation with other properties

### Conjunction with other properties

- Trim subgroup property: This is the conjunction of being trivially true and identity-true

### Opposites

A metaproperty that is almost the negative of being trivially true subgroup property, is that of being trivially collapsed.