# Direct factor implies normal

From Groupprops

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., direct factor) must also satisfy the second subgroup property (i.e., normal subgroup)

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## Statement

Suppose is an internal direct product of subgroups and , so that both and are direct factors of . Then, both and are normal subgroups of .

## Intermediate properties

## Proof

The proof is direct from the definition.