Pronormal implies weakly normal

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., pronormal subgroup) must also satisfy the second subgroup property (i.e., weakly normal subgroup)
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Statement

Any pronormal subgroup of a group is a weakly normal subgroup.

Definitions used

Pronormal subgroup

Further information: Pronormal subgroup

Weakly normal subgroup

Further information: Weakly normal subgroup

Facts used

1. Pronormal implies paranormal
2. Paranormal implies weakly normal

Proof

Proof from given facts

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

Hands-on proof

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