Trivial subgroup
From Groupprops
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.