# Group in which every subgroup is subnormal

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

## Contents

## Definition

A **group in which every subgroup is subnormal** is a group with the property that every subgroup is a subnormal subgroup.

## Relation with other properties

### Stronger properties

- Nilpotent group:
*For proof of the implication, refer Nilpotent implies every subgroup is subnormal and for proof of its strictness (i.e. the reverse implication being false) refer Every subgroup is subnormal not implies nilpotent*.

### Weaker properties

- Gruenberg group:
*For proof of the implication, refer Every subgroup is subnormal implies Gruenberg and for proof of its strictness (i.e. the reverse implication being false) refer Gruenberg not implies every subgroup is subnormal*. - Group satisfying normalizer condition:
*For proof of the implication, refer Every subgroup is subnormal implies normalizer condition and for proof of its strictness (i.e. the reverse implication being false) refer Normalizer condition not implies every subgroup is subnormal*. - Group in which every maximal subgroup is normal