Group in which every characteristic subgroup is strictly characteristic
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
Note that since characteristic not implies strictly characteristic, not all groups have this property.
In terms of the subgroup property collapse operator
This group property can be defined in terms of the collapse of two subgroup properties. In other words, a group satisfies this group property if and only if every subgroup of it satisfying the first property (characteristic subgroup) satisfies the second property (strictly characteristic subgroup), and vice versa.
View other group properties obtained in this way
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse impliation failure)||Intermediate notions|
|Hopfian group||every surjective endomorphism is an automorphism|||FULL LIST, MORE INFO|
|Group in which every characteristic subgroup is fully invariant||every characteristic subgroup is a fully invariant subgroup|||FULL LIST, MORE INFO|
|Characteristically simple group||nontrivial; no proper nontrivial characteristic subgroup|||FULL LIST, MORE INFO|