Group with no proper nontrivial marginal subgroup
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 |