NE implies weakly normal
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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., NE-subgroup) must also satisfy the second subgroup property (i.e., weakly normal subgroup)
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Further information: NE-subgroup
Weakly normal subgroup
Further information: Weakly normal subgroup
A subgroup of a group is termed a weakly normal subgroup of if any conjugate of that is contained in is actually contained in .
Given: A group , a subgroup such that . A conjugate of such that .
To prove: .
Proof: By definition of normal closure, . Thus, we get , so .