# Normal not implies strongly potentially characteristic

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This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., normal subgroup) need not satisfy the second subgroup property (i.e., strongly potentially characteristic subgroup)
View a complete list of subgroup property non-implications | View a complete list of subgroup property implications
Get more facts about normal subgroup|Get more facts about strongly potentially characteristic subgroup
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## Verbal statement=

A normal subgroup need not be strongly potentially characteristic.

### Statement with symbols

It is possible to have a group $K$ and a normal subgroup $H$ of $K$ such that there is no group $G$ containing $K$ in which both $H$ and $K$ are characteristic subgroups.

## Proof

The proof follows directly from facts (1) and (2).