Group in which every subgroup has a subnormalizer

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

A group in which every subgroup has a subnormalizer is a group in which every subgroup has a subnormalizer; in other words, every subgroup is a subgroup having a subnormalizer.

Not every group is of this kind because subnormality is not upper join-closed (specifically, any counterexample to subnormality not being upper join-closed gives a subgroup of a group that does not have a subnormalizer).

Relation with other properties

Stronger properties