Left-transitively WNSCDIN not implies normal

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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., left-transitively WNSCDIN-subgroup) need not satisfy the second subgroup property (i.e., normal subgroup)
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Get more facts about left-transitively WNSCDIN-subgroup|Get more facts about normal subgroup
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Statement

We can have a group G and a left-transitively WNSCDIN-subgroup H of G that is not normal in G.

Proof

Example of a subgroup of order two

Further information: dihedral group:D8

Let G be any group with a non-normal subgroup H of order two. Then, H is left-transitively WNSCDIN in G.

For a concrete example, take G to be a dihedral group and H to be a subgroup of order two generated by a reflection element.