# 2-subnormality is conjugate-join-closed

From Groupprops

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

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

Get more facts about 2-subnormal subgroup |Get facts that use property satisfaction of 2-subnormal subgroup | Get facts that use property satisfaction of 2-subnormal subgroup|Get more facts about conjugate-join-closed subgroup property

## Statement

A join of any collection of 2-subnormal subgroups that are conjugate to each other is also a 2-subnormal subgroup.

## Related facts

- Normality is strongly join-closed: An arbitrary join of normal subgroups is normal.
- Subnormality is normalizing join-closed
- 3-subnormal implies finite-conjugate-join-closed subnormal