Subgroup whose normalizer equals its normal closure
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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: tightly 2-subnormal subgroup and 2-hypernormalized subgroup
View other subgroup property conjunctions | view all subgroup properties
- The normalizer of in equals the normal closure of in .
- It is both a 2-hypernormalized subgroup (its normalizer is normal) and a subgroup with unique 2-subnormal series (it has a unique subnormal series of length two).
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|2-hypernormalized subgroup||normalizer is normal|||FULL LIST, MORE INFO|
|Subgroup with unique 2-subnormal series||has unique subnormal series of length two; equivalently, its normal closure is the normal core of its normalizer|||FULL LIST, MORE INFO|
|2-subnormal subgroup||normal subgroup of normal subgroup|||FULL LIST, MORE INFO|