# Pronormality satisfies intermediate subgroup condition

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This article gives the statement, and possibly proof, of a subgroup property (i.e., pronormal subgroup) satisfying a subgroup metaproperty (i.e., intermediate subgroup condition)

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## Statement

### Statement with symbols

Suppose are groups such that is a pronormal subgroup of . Then, is also a pronormal subgroup of .

## Related facts

### Related metaproperty dissatisfactions for pronormality

- Pronormality does not satisfy transfer condition: We can have a pronormal subgroup of and a subgroup of such that is not pronormal in .
- Pronormality is not upper join-closed: If is pronormal in intermediate subgroups , it is
*not*necessary that is pronormal in .

### Related properties satisfying the intermediate subgroup condition

- Weak pronormality satisfies intermediate subgroup condition
- Paranormality satisfies intermediate subgroup condition
- Polynormality satisfies intermediate subgroup condition
- Weak normality satisfies intermediate subgroup condition

## Proof

This is direct from the definition.**PLACEHOLDER FOR INFORMATION TO BE FILLED IN**: [SHOW MORE]