Polynormality is strongly join-closed
This article gives the statement, and possibly proof, of a subgroup property (i.e., polynormal subgroup) satisfying a subgroup metaproperty (i.e., strongly join-closed subgroup property)
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Statement
The join of an arbitrary (possibly empty) collection of polynormal subgroups of a group is again polynormal.
Related facts
- Paranormality is strongly join-closed
- Paracharacteristicity is strongly join-closed
- Polycharacteristicity is strongly join-closed