Group in which every subgroup has a subnormalizer

Definition
A group in which every subgroup has a subnormalizer is a group in which every subgroup has a defining ingredient::subnormalizer; in other words, every subgroup is a defining ingredient::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).

Stronger properties

 * Weaker than::Nilpotent group
 * Weaker than::Group in which every subgroup is subnormal
 * Weaker than::Group in which every subgroup is pronormal
 * Weaker than::T*-group