# Intermediately automorph-conjugate of normal implies weakly pronormal

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., intermediately automorph-conjugate subgroup of normal subgroup) must also satisfy the second subgroup property (i.e., weakly pronormal subgroup)

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## Contents

## Statement

### Property-theoretic statement

The subgroup property of being an intermediately automorph-conjugate subgroup of normal subgroup (i.e., the property obtained by applying the composition operator to the properties of intermediately automorph-conjugate subgroup and normal subgroup) is *stronger than* the subgroup property of being a weakly pronormal subgroup.

### Verbal statement

Any Intermediately automorph-conjugate subgroup (?) of a Normal subgroup (?) of a group is weakly pronormal.