This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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A group in which every nontrivial normal subgroup has finite index is a group with the property that every nontrivial normal subgroup (i.e., every normal subgroup other than the trivial subgroup) is a subgroup of finite index: in other words, its index in the whole group is finite.
Relation with other properties