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- Component_(group_theory) abstract "In mathematics, in the field of group theory, a component of a finite group is a quasisimple subnormal subgroup. Any two distinct components commute. The product of all the components is the layer of the group.For finite abelian (or nilpotent) groups, p-component is used in a different sense to mean the Sylow p-subgroup, so the abelian group is the product of its p-components for primes p. These are not components in the sense above, as abelian groups are not quasisimple.A quasisimple subgroup of a finite group is called a standard component if its centralizer has even order, it is normal in the centralizer of every involution centralizing it, and it commutes with none of its conjugates. This concept is used in the classification of finite simple groups, for instance, by showing that under mild restrictions on the standard component one of the following always holds: a standard component is normal (so a component as above), the whole group has a nontrivial solvable normal subgroup, the subgroup generated by the conjugates of the standard component is on a short list, or the standard component is a previously unknown quasisimple group (Aschbacher & Seitz 1976).".
- Component_(group_theory) wikiPageID "4939168".
- Component_(group_theory) wikiPageLength "2055".
- Component_(group_theory) wikiPageOutDegree "19".
- Component_(group_theory) wikiPageRevisionID "368973842".
- Component_(group_theory) wikiPageWikiLink Abelian_group.
- Component_(group_theory) wikiPageWikiLink Category:Group_theory.
- Component_(group_theory) wikiPageWikiLink Category:Subgroup_properties.
- Component_(group_theory) wikiPageWikiLink Centralizer.
- Component_(group_theory) wikiPageWikiLink Centralizer_and_normalizer.
- Component_(group_theory) wikiPageWikiLink Classification_of_finite_simple_groups.
- Component_(group_theory) wikiPageWikiLink Commutative_property.
- Component_(group_theory) wikiPageWikiLink Commutativity.
- Component_(group_theory) wikiPageWikiLink Conjugacy_class.
- Component_(group_theory) wikiPageWikiLink Finite_group.
- Component_(group_theory) wikiPageWikiLink Fitting_subgroup.
- Component_(group_theory) wikiPageWikiLink Group_(mathematics).
- Component_(group_theory) wikiPageWikiLink Group_theory.
- Component_(group_theory) wikiPageWikiLink Involution_(mathematics).
- Component_(group_theory) wikiPageWikiLink Mathematics.
- Component_(group_theory) wikiPageWikiLink Nilpotent_group.
- Component_(group_theory) wikiPageWikiLink Normal_subgroup.
- Component_(group_theory) wikiPageWikiLink Quasisimple_group.
- Component_(group_theory) wikiPageWikiLink Solvable_group.
- Component_(group_theory) wikiPageWikiLink Subnormal_subgroup.
- Component_(group_theory) wikiPageWikiLink Sylow_theorems.
- Component_(group_theory) wikiPageWikiLinkText "''p''-components".
- Component_(group_theory) wikiPageWikiLinkText "Component (group theory)".
- Component_(group_theory) wikiPageWikiLinkText "component".
- Component_(group_theory) wikiPageWikiLinkText "components".
- Component_(group_theory) hasPhotoCollection Component_(group_theory).
- Component_(group_theory) wikiPageUsesTemplate Template:Citation.
- Component_(group_theory) wikiPageUsesTemplate Template:Harv.
- Component_(group_theory) subject Category:Group_theory.
- Component_(group_theory) subject Category:Subgroup_properties.
- Component_(group_theory) hypernym Subgroup.
- Component_(group_theory) type EthnicGroup.
- Component_(group_theory) comment "In mathematics, in the field of group theory, a component of a finite group is a quasisimple subnormal subgroup. Any two distinct components commute. The product of all the components is the layer of the group.For finite abelian (or nilpotent) groups, p-component is used in a different sense to mean the Sylow p-subgroup, so the abelian group is the product of its p-components for primes p.".
- Component_(group_theory) label "Component (group theory)".
- Component_(group_theory) sameAs m.0cw40v.
- Component_(group_theory) sameAs Q5156688.
- Component_(group_theory) sameAs Q5156688.
- Component_(group_theory) wasDerivedFrom Component_(group_theory)?oldid=368973842.
- Component_(group_theory) isPrimaryTopicOf Component_(group_theory).