# Group in which every normal subgroup is fully invariant

From Groupprops

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 propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Contents

## Definition

### Symbol-free definition

A **group in which every normal subgroup is fully characteristic** or **group in which every normal subgroup is fully characteristic** is a group with the property that every normal subgroup of the group is fully invariant in it.

## 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 (normal subgroup) satisfies the second property (fully invariant subgroup), and vice versa.

View other group properties obtained in this way

The property can be expressed as the collapse of the following subgroup properties: normal subgroup = fully invariant subgroup