Nilpotent normal subgroup

From Groupprops
Revision as of 16:04, 19 May 2008 by Vipul (talk | contribs) (New page: {{group-subgroup property conjunction|normal subgroup|nilpotent group}} ==Definition== ===Symbol-free definition=== A subgroup of a group is termed a '''nilpotent normal subgrou...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
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

Definition

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

Facts

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.