# Characteristic transitively normal subgroup

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and transitively normal subgroup
View other subgroup property conjunctions | view all subgroup properties
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and CEP-subgroup
View other subgroup property conjunctions | view all subgroup properties

## Definition

A subgroup of a group is termed a characteristic transitively normal subgroup if it satisfies the following equivalent conditions:

1. It is both a characteristic subgroup and a transitively normal subgroup.
2. It is both a characteristic subgroup and a CEP-subgroup.

## 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

### Trimness

This subgroup property is trim -- it is both trivially true (true for the trivial subgroup) and identity-true (true for a group as a subgroup of itself).
View other trim subgroup properties | View other trivially true subgroup properties | View other identity-true subgroup properties