Maximal implies pronormal

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

Any maximal subgroup of a group must be a pronormal subgroup.

Facts used

  1. Maximal implies normal or abnormal
  2. Normal implies pronormal
  3. Abnormal implies pronormal

Proof

The proof follows by piecing together facts (1), (2) and (3).