Group with no proper nontrivial marginal subgroup

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Definition

A group with no proper nontrivial marginal subgroup is a nontrivial group with the property that the only marginal subgroups of the group are the whole group and the trivial subgroup.

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
simple group
characteristically simple group
free abelian group
torsion-free abelian group