Index four implies 2-subnormal or double coset index two

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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 must also satisfy the second subgroup property
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Any Subgroup of index four (?) (i.e., a subgroup of a group whose index in the whole group is four) is either 2-subnormal or has double coset index two.

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