# Difference between revisions of "Group in which every maximal subgroup is normal"

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 properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of nilpotence|Find other variations of nilpotence | Read a survey article on varying nilpotence

## Definition

A group in which every maximal subgroup is normal is a group satisfying the following equivalent conditions:

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
nilpotent group has a central series of finite length nilpotent implies every maximal subgroup is normal every maximal subgroup is normal not implies nilpotent Group in which every subgroup is subnormal, Group satisfying normalizer condition|FULL LIST, MORE INFO
group in which every subgroup is subnormal every subgroup is a subnormal subgroup every subgroup is subnormal implies every maximal subgroup is normal Group satisfying normalizer condition|FULL LIST, MORE INFO
hypercentral group hypercenter of the group (the point at which the transfinite upper central series stabilizes) is the whole group hypercentral implies every maximal subgroup is normal every maximal subgroup is normal not implies hypercentral |FULL LIST, MORE INFO
group satisfying normalizer condition there is no proper self-normalizing subgroup normalizer condition implies every maximal subgroup is normal every maximal subgroup is normal not implies normalizer condition |FULL LIST, MORE INFO