Trivially true subgroup property

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