Group in which every nontrivial normal subgroup has finite index

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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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Definition

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

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finite group |FULL LIST, MORE INFO
simple group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
group in which every normal subgroup is finite or has finite index |FULL LIST, MORE INFO
residually finite group unless the group is simple

Facts