# Group in which every normal subgroup is a direct factor

From Groupprops

## Contents

## Definition

A **group in which every normal subgroup is a direct factor** is a group with the property that every normal subgroup of the group is a direct factor 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 (normal subgroup) satisfies the second property (direct factor), and vice versa.

View other group properties obtained in this way