Hirsch-Plotkin radical

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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Definition

Symbol-free definition

The Hirsch-Plotkin radical of a group is defined as the subgroup generated by all its normal locally nilpotent subgroups.

Relation with other subgroup-defining functions

Smaller subgroup-defining functions

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