# Characteristic subgroup of direct factor

From Groupprops

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This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: characteristic subgroup and direct factor

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## Definition

### Symbol-free definition

A subgroup of a group is said to be a **characteristic subgroup of direct factor** if it occurs as a characteristic subgroup of a direct factor of the whole group.

### Definition with symbols

A subgroup of a group is said to be a **characteristic subgroup of direct factor** if there are subgroups such that is characteristic in , and .