# Subnormality is not permuting upper join-closed

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., subnormal subgroup)notsatisfying a subgroup metaproperty (i.e., permuting upper join-closed subgroup property).

View all subgroup metaproperty dissatisfactions | View all subgroup metaproperty satisfactions|Get help on looking up metaproperty (dis)satisfactions for subgroup properties

Get more facts about subnormal subgroup|Get more facts about permuting upper join-closed subgroup property|

This article gives the statement, and possibly proof, of a subgroup property (i.e., 2-subnormal subgroup)notsatisfying a subgroup metaproperty (i.e., permuting upper join-closed subgroup property).

View all subgroup metaproperty dissatisfactions | View all subgroup metaproperty satisfactions|Get help on looking up metaproperty (dis)satisfactions for subgroup properties

Get more facts about 2-subnormal subgroup|Get more facts about permuting upper join-closed subgroup property|

## Statement

It is possible to have a group , a subgroup of , and intermediate subgroups and of containing such that is a 2-subnormal subgroup in both and , (i.e., they are permuting subgroups), but is *not* a subnormal subgroup of .

## Related facts

- Subnormality is permuting upper join-closed in finite
- Subnormality is not upper join-closed
- 2-subnormality is not upper join-closed

## References

### Journal references

- Paper:CasoloDardano04
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