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- Hirsch–Plotkin_radical abstract "In mathematics, especially in the study of infinite groups, the Hirsch–Plotkin radical is a subgroup describing the normal nilpotent subgroups of the group. It was named by Gruenberg (1961) after Kurt Hirsch and Boris I. Plotkin, who proved that the product of locally nilpotent groups remains locally nilpotent; this fact is a key ingredient in its construction.The Hirsch–Plotkin radical is defined as the subgroup generated by the union of the normal locally nilpotent subgroups (that is, those normal subgroups such that every finitely generated subgroup is nilpotent). The Hirsch–Plotkin radical is itself a locally nilpotent normal subgroup, so is the unique largest such. The Hirsch–Plotkin radical generalizes the Fitting subgroup to infinite groups. Unfortunately the subgroup generated by the union of infinitely many normal nilpotent subgroups need not itself be nilpotent, so the Fitting subgroup must be modified in this case.".
- Hirsch–Plotkin_radical wikiPageID "22468906".
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- Hirsch–Plotkin_radical wikiPageRevisionID "621323986".
- Hirsch–Plotkin_radical wikiPageWikiLink Category:Functional_subgroups.
- Hirsch–Plotkin_radical wikiPageWikiLink Category:Infinite_group_theory.
- Hirsch–Plotkin_radical wikiPageWikiLink Fitting_subgroup.
- Hirsch–Plotkin_radical wikiPageWikiLink Group_(mathematics).
- Hirsch–Plotkin_radical wikiPageWikiLink Kurt_Hirsch.
- Hirsch–Plotkin_radical wikiPageWikiLink Mathematics.
- Hirsch–Plotkin_radical wikiPageWikiLink Nilpotent_group.
- Hirsch–Plotkin_radical wikiPageWikiLink Normal_subgroup.
- Hirsch–Plotkin_radical wikiPageWikiLink Subgroup.
- Hirsch–Plotkin_radical wikiPageWikiLinkText "Hirsch–Plotkin radical".
- Hirsch–Plotkin_radical hasPhotoCollection Hirsch–Plotkin_radical.
- Hirsch–Plotkin_radical wikiPageUsesTemplate Template:Algebra-stub.
- Hirsch–Plotkin_radical wikiPageUsesTemplate Template:Harvtxt.
- Hirsch–Plotkin_radical wikiPageUsesTemplate Template:Reflist.
- Hirsch–Plotkin_radical subject Category:Functional_subgroups.
- Hirsch–Plotkin_radical subject Category:Infinite_group_theory.
- Hirsch–Plotkin_radical comment "In mathematics, especially in the study of infinite groups, the Hirsch–Plotkin radical is a subgroup describing the normal nilpotent subgroups of the group. It was named by Gruenberg (1961) after Kurt Hirsch and Boris I.".
- Hirsch–Plotkin_radical label "Hirsch–Plotkin radical".
- Hirsch–Plotkin_radical sameAs m.05zr8yk.
- Hirsch–Plotkin_radical sameAs Q16944859.
- Hirsch–Plotkin_radical sameAs Q16944859.
- Hirsch–Plotkin_radical wasDerivedFrom Hirsch–Plotkin_radical?oldid=621323986.
- Hirsch–Plotkin_radical isPrimaryTopicOf Hirsch–Plotkin_radical.