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