Nilpotent join of intermediately isomorph-conjugate subgroups is intermediately isomorph-conjugate

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Statement

Suppose H_1, H_2 \le G are Intermediately isomorph-conjugate subgroup (?)s, such that \langle H_1, H_2 \rangle is a Nilpotent group (?). Then, \langle H_1, H_2 \rangle is also intermediately isomorph-conjugate.

Related facts

Similar facts

Facts used

  1. Intermediate isomorph-conjugacy is normalizing join-closed
  2. Nilpotent implies every subgroup is subnormal
  3. Intermediately isomorph-conjugate implies intermediately subnormal-to-normal

Proof

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