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

From Groupprops

## Statement

Suppose are Intermediately isomorph-conjugate subgroup (?)s, such that is a Nilpotent group (?). Then, is also intermediately isomorph-conjugate.

## Related facts

### Similar facts

## Facts used

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

## Proof

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