# Group with no proper nontrivial marginal subgroup

From Groupprops

## 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 propertiesVIEW 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 |