About: Central series

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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.

Attributes	Values
rdfs:label	Central series (en)
rdfs: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. This article uses the language of group theory; analogous terms are used for Lie algebras. (en)
dct:subject	Subgroup series
Wikipage page ID	15202655 (xsd:integer)
Wikipage revision ID	1070866444 (xsd:integer)
Link from a Wikipage to another Wikipage	Elementary abelian group Engel's theorem Normal series Derived subgroup Derived series Descendant tree (group theory) Lie theory Limit ordinal Stephen Arthur Jennings Periodic group Commutator Mathematics Ordinal numbers Lower Fitting series Generating set of a group Combinatorial group theory Commutator subgroup Frattini subgroup Perfect group Subgroup Matrix ring Center (group theory) Cyclic group Nilpotent group Subgroup series Direct product Direct sum of groups Quaternion group Group (mathematics) Adjoint representation of a Lie group Sylow subgroup Transfinite recursion Socle (mathematics) Free group Group ring Group theory Factor group Solvable group Symmetric group Flag (linear algebra) P-group Nilpotent series Residually nilpotent Upper triangular Lie subalgebra Center (group) Centerless group Grün's lemma Unipotent group Exponent (group theory) Loewy series
sameAs	Central series Central series Central series
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:More_citations_needed dbt:Short_description
has 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, despite the "central" in their names, central series if and only if a group is nilpotent. (en)
gold:hypernym	Kind
prov:wasDerivedFrom	wikipedia-en:Central_series?oldid=1070866444&ns=0
page length (characters) of wiki page	13793 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Central_series
is Link from a Wikipage to another Wikipage of	Descendant tree (group theory) Z-group Lower Central Series Alexander Skopin Lie algebra Lower central series Commutator collecting process Perfect group Nilpotent space Nilpotent group Fitting length Subgroup series Urs Stammbach Upper Central Series Upper central series Hypocentral group Jennings series Hypercenter Hypercentral group Nilpotent residual
is Wikipage redirect of	Lower Central Series Lower central series Upper Central Series Upper central series Hypocentral group Jennings series Hypercenter Hypercentral group Nilpotent residual
is foaf:primaryTopic of	wikipedia-en:Central_series

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