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Finite nilpotent group
From Groupprops
This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)
View other properties of finite groups OR View all group properties
Contents |
Definition
Symbol-free definition
A finite group is termed a finite nilpotent group if it satisfies the following equivalent conditions:
- It is a nilpotent group
- It satisfies the normalizer condition i.e. it has no proper self-normalizing subgroup
- Every maximal subgroup is normal
- All its Sylow subgroups are normal
- It is the direct product of its Sylow subgroups
Relation with other properties
Stronger properties
Weaker properties
