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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 1 Definition 1.1 Symbol-free definition 2 Examples 3 Relation with other properties 3.1 Stronger properties 3.2 Weaker properties

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

Examples

VIEW: groups satisfying this property | groups dissatisfying property finite group | groups dissatisfying property nilpotent group
VIEW: |

Relation with other properties

Stronger properties

Weaker properties

• Finite solvable group