Trivially true subgroup property

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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 metaproperty
VIEW 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

Opposites

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