# Paranormality is strongly join-closed

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., paranormal subgroup) satisfying a subgroup metaproperty (i.e., strongly join-closed subgroup property)

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Get more facts about paranormal subgroup |Get facts that use property satisfaction of paranormal subgroup | Get facts that use property satisfaction of paranormal subgroup|Get more facts about strongly join-closed subgroup property

## Statement

The join of an arbitrary (possibly empty) collection of paranormal subgroups of a group is again paranormal.

## Related facts

- Polynormality is strongly join-closed
- Paracharacteristicity is strongly join-closed
- Polycharacteristicity is strongly join-closed