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

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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 $K$.

## 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