Double coset index two implies maximal
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., subgroup of double coset index two) must also satisfy the second subgroup property (i.e., maximal subgroup)
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- Index three implies normal or double coset index two
- Index four implies 2-subnormal or double coset index two
The idea is that any intermediate subgroup containing the given subgroup must be a union of double cosets of the subgroup.