Trivial subgroup

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]

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VIEW RELATED: Subgroup property implications | Subgroup property non-implications | Subgroup metaproperty satisfactions | Subgroup metaproperty dissatisfactions | Subgroup property satisfactions |Subgroup property dissatisfactions
VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

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.