Locally nilpotent normal subgroup

From Groupprops
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): locally nilpotent group
View a complete list of such conjunctions

Definition

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

Facts

  • The subgroup generated by all locally nilpotent normal subgroups is the unique largest locally nilpotent normal subgroup of the group, and is termed the Hirsch-Plotkin radical of the group.