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- Central_series abstract "In mathematics, especially in the fields of group theory and Lie theory, a central series is a kind of normal series of subgroups or Lie subalgebras, expressing the idea that the commutator is nearly trivial. For groups, this is an explicit expression that the group is a nilpotent group, and for matrix rings, this is an explicit expression that in some basis the matrix ring consists entirely of upper triangular matrices with constant diagonal. This article uses the language of group theory; analogous terms are used for Lie algebras.The lower central series and upper central series (also called the descending central series and ascending central series, respectively), are characteristic series, which, despite the names, are central series if and only if a group is nilpotent.".
- Central_series wikiPageID "15202655".
- Central_series wikiPageLength "12585".
- Central_series wikiPageOutDegree "58".
- Central_series wikiPageRevisionID "618860221".
- Central_series wikiPageWikiLink Adjoint_representation.
- Central_series wikiPageWikiLink Adjoint_representation_of_a_Lie_group.
- Central_series wikiPageWikiLink Category:Subgroup_series.
- Central_series wikiPageWikiLink Center_(group).
- Central_series wikiPageWikiLink Center_(group_theory).
- Central_series wikiPageWikiLink Centerless_group.
- Central_series wikiPageWikiLink Characteristic_series.
- Central_series wikiPageWikiLink Combinatorial_group_theory.
- Central_series wikiPageWikiLink Commutator_subgroup.
- Central_series wikiPageWikiLink Derived_series.
- Central_series wikiPageWikiLink Derived_subgroup.
- Central_series wikiPageWikiLink Descendant_tree_(group_theory).
- Central_series wikiPageWikiLink Direct_sum_of_groups.
- Central_series wikiPageWikiLink Elementary_abelian_group.
- Central_series wikiPageWikiLink Engels_theorem.
- Central_series wikiPageWikiLink Exponent_(group_theory).
- Central_series wikiPageWikiLink Factor_group.
- Central_series wikiPageWikiLink Fitting_length.
- Central_series wikiPageWikiLink Flag_(linear_algebra).
- Central_series wikiPageWikiLink Frattini_subgroup.
- Central_series wikiPageWikiLink Free_group.
- Central_series wikiPageWikiLink Generating_set_of_a_group.
- Central_series wikiPageWikiLink Group_(mathematics).
- Central_series wikiPageWikiLink Group_ring.
- Central_series wikiPageWikiLink Group_theory.
- Central_series wikiPageWikiLink Grxc3xbcns_lemma.
- Central_series wikiPageWikiLink Lie_algebra.
- Central_series wikiPageWikiLink Lie_subalgebra.
- Central_series wikiPageWikiLink Lie_theory.
- Central_series wikiPageWikiLink Limit_ordinal.
- Central_series wikiPageWikiLink Loewy_ring.
- Central_series wikiPageWikiLink Loewy_series.
- Central_series wikiPageWikiLink Lower_Fitting_series.
- Central_series wikiPageWikiLink Mathematics.
- Central_series wikiPageWikiLink Matrix_ring.
- Central_series wikiPageWikiLink Nilpotent_group.
- Central_series wikiPageWikiLink Nilpotent_series.
- Central_series wikiPageWikiLink Normal_series.
- Central_series wikiPageWikiLink Ordinal_number.
- Central_series wikiPageWikiLink Ordinal_numbers.
- Central_series wikiPageWikiLink P-group.
- Central_series wikiPageWikiLink Perfect_group.
- Central_series wikiPageWikiLink Periodic_group.
- Central_series wikiPageWikiLink Quotient_group.
- Central_series wikiPageWikiLink Residual_property_(mathematics).
- Central_series wikiPageWikiLink Residually_nilpotent.
- Central_series wikiPageWikiLink S._A._Jennings.
- Central_series wikiPageWikiLink Socle_(mathematics).
- Central_series wikiPageWikiLink Solvable_group.
- Central_series wikiPageWikiLink Stephen_Arthur_Jennings.
- Central_series wikiPageWikiLink Subgroup.
- Central_series wikiPageWikiLink Subgroup_series.
- Central_series wikiPageWikiLink Sylow_subgroup.
- Central_series wikiPageWikiLink Sylow_theorems.
- Central_series wikiPageWikiLink Torsion_group.
- Central_series wikiPageWikiLink Transfinite_induction.
- Central_series wikiPageWikiLink Transfinite_recursion.
- Central_series wikiPageWikiLink Triangular_matrix.
- Central_series wikiPageWikiLink Upper_triangular.
- Central_series wikiPageWikiLinkText "Central series".
- Central_series wikiPageWikiLinkText "Central series#Lower central series".
- Central_series wikiPageWikiLinkText "Central series#Upper central series".
- Central_series wikiPageWikiLinkText "Central_series#Refined_central_series".
- Central_series wikiPageWikiLinkText "central series".
- Central_series wikiPageWikiLinkText "centre".
- Central_series wikiPageWikiLinkText "lower central series".
- Central_series wikiPageWikiLinkText "lower exponent-p central series".
- Central_series wikiPageWikiLinkText "upper central series".
- Central_series hasPhotoCollection Central_series.
- Central_series wikiPageUsesTemplate Template:Citation.
- Central_series wikiPageUsesTemplate Template:Harv.
- Central_series wikiPageUsesTemplate Template:Refimprove.
- Central_series subject Category:Subgroup_series.
- Central_series hypernym Kind.
- Central_series type Article.
- Central_series type Article.
- Central_series comment "In mathematics, especially in the fields of group theory and Lie theory, a central series is a kind of normal series of subgroups or Lie subalgebras, expressing the idea that the commutator is nearly trivial. For groups, this is an explicit expression that the group is a nilpotent group, and for matrix rings, this is an explicit expression that in some basis the matrix ring consists entirely of upper triangular matrices with constant diagonal.".
- Central_series label "Central series".
- Central_series sameAs Suite_centrale_descendante.
- Central_series sameAs m.03hlqvd.
- Central_series sameAs Q5062152.
- Central_series sameAs Q5062152.
- Central_series wasDerivedFrom Central_series?oldid=618860221.
- Central_series isPrimaryTopicOf Central_series.