This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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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 with symbols
Note that if the group itself is trivial, it cannot have any nontrivial subgroup.
The opposite of the property of being nontrivial is the property of being trivial, i.e. being the subgroup comprising only the identity element.