Hirsch-Plotkin radical

Definition
The Hirsch-Plotkin radical of a group can be defined in the following equivalent ways:


 * 1) It is the subgroup generated by all the locally nilpotent normal subgroups (i.e., normal locally nilpotent subgroups) of the group.
 * 2) It is the unique largest locally nilpotent normal subgroup of the group.
 * 3) It is the subgroup generated by all the locally nilpotent characteristic subgroups (i.e., characteristic locally nilpotent subgroups) of the group.
 * 4) It is the unique largest locally nilpotent characteristic subgroup of the group.

Smaller subgroup-defining functions

 * Fitting subgroup (they become equal in case the group is finite)