Nilpotent normal subgroup

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This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): nilpotent group
View a complete list of such conjunctions


Symbol-free definition

A subgroup of a group is termed a nilpotent normal subgroup if it is nilpotent as a group, and normal as a subgroup.

Relation with other properties

Stronger properties

Weaker properties


The subgroup of a group generated by all its nilpotent normal subgroups is termed the Fitting subgroup, and if a group equals its Fitting subgroup, then it is termed a Fitting group. For finite groups, the Fitting subgroup is the largest nilpotent normal subgroup, and a Fitting group is the same thing as a nilpotent group.