Hirsch-Plotkin radical

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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.
This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
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This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
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Relation with other subgroup-defining functions

Smaller subgroup-defining functions