# Group in which every subgroup has a subnormalizer

From Groupprops

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

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## 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).