Subgroup in which every subgroup characteristic in the whole group is characteristic

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

Suppose K \le G is a subgroup. We say that K is a subgroup in which every subgroup characteristic in the whole group is characteristic if, for any subgroup H \le K such that H is a characteristic subgroup of G, H is also a characteristic subgroup of K.

Relation with other properties

Stronger properties

Metaproperties

Transitivity

This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.
ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitive
ABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity