Sylow implies intermediately isomorph-conjugate

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This article gives the statement and possibly, proof, of an implication relation between two subgroup properties, when the big group is a finite group. That is, it states that in a Finite group (?), every subgroup satisfying the first subgroup property (i.e., Sylow subgroup (?)) must also satisfy the second subgroup property (i.e., Intermediately isomorph-conjugate subgroup (?)). In other words, every Sylow subgroup of finite group is a intermediately isomorph-conjugate subgroup of finite group.
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Statement

A Sylow subgroup of a finite group is intermediately isomorph-conjugate: it is isomorph-conjugate in every intermediate subgroup.

Facts used

  1. Sylow satisfies intermediate subgroup condition: A Sylow subgroup of a group is Sylow in every intermediate subgroup.
  2. Sylow implies isomorph-conjugate

Proof

The proof follows directly by combining facts (1) and (2).