The Hirsch-Plotkin radical of a group can be defined in the following equivalent ways:
- It is the subgroup generated by all the locally nilpotent normal subgroups (i.e., normal locally nilpotent subgroups) of the group.
- It is the unique largest locally nilpotent normal subgroup of the group.
- It is the subgroup generated by all the locally nilpotent characteristic subgroups (i.e., characteristic locally nilpotent subgroups) of the group.
- 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
View a complete list of subgroup-defining functions OR View a complete list of quotient-defining functions
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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View a list of other standard non-basic definitions
Relation with other subgroup-defining functions
Smaller subgroup-defining functions
- Fitting subgroup (they become equal in case the group is finite)