Hall implies paracharacteristic

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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., Hall subgroup) must also satisfy the second subgroup property (i.e., paracharacteristic subgroup)
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Related facts

Corollaries

Facts used

  1. Hall implies join of Sylow subgroups
  2. Sylow implies paracharacteristic
  3. Paracharacteristicity is strongly join-closed