Normalizer-relatively normal subgroup
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This article describes a property that can be evaluated for a triple of a group, a subgroup of the group, and a subgroup of that subgroup.
View other such properties
Suppose are groups. We say that is a normalizer-relatively normal subgroup of with respect to if the following equivalent conditions are satisfied:
- Whenever is such that is normal in , is also normal in .
- The normalizer is contained in the normalizer .
- is normal in .
Relation with other properties
- Middle-characteristic subgroup
- Strongly closed subgroup
- Weakly closed subgroup: For full proof, refer: Weakly closed implies normalizer-relatively normal