Group in which every characteristic subgroup is fully invariant

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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 characteristic subgroup is fully characteristic is a group with the property that every characteristic subgroup of it is fully characteristic -- it is invariant under all endomorphisms of the group.

Formalisms

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 (fully characteristic subgroup), and vice versa.
View other group properties obtained in this way

Relation with other properties

Stronger properties