About: Hirsch–Plotkin radical

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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 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.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Group100031264 yago:WikicatFunctionalSubgroups ethnic group yago:Subgroup108001083
rdfs:label	Hirsch–Plotkin radical (en)
rdfs: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 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. (en)
dcterms:subject	Infinite group theory Functional subgroups
Wikipage page ID	22468906 (xsd:integer)
Wikipage revision ID	1089123009 (xsd:integer)
Link from a Wikipage to another Wikipage	Kurt Hirsch Mathematics Normal subgroup Subgroup Infinite group theory Nilpotent group Functional subgroups Mathematical proof Group (mathematics) Direct product of groups Union (set theory) Fitting subgroup Finitely generated subgroup
sameAs	Hirsch–Plotkin radical Hirsch–Plotkin radical Hirsch–Plotkin radical
dbp:wikiPageUsesTemplate	dbt:Algebra-stub dbt:Harvtxt dbt:Reflist
has 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 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. (en)
gold:hypernym	Subgroup
prov:wasDerivedFrom	wikipedia-en:Hirsch–Plotkin_radical?oldid=1089123009&ns=0
page length (characters) of wiki page	3495 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Hirsch–Plotkin_radical
is Link from a Wikipage to another Wikipage of	Kurt Hirsch Locally nilpotent Radical of a ring Hirsch-Plotkin radical
is Wikipage redirect of	Hirsch-Plotkin radical
is foaf:primaryTopic of	wikipedia-en:Hirsch–Plotkin_radical

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