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Central series

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, the existence of a central series means it is a nilpotent group; for matrix rings (considered as Lie algebras), it means that in some…

Lower central series, Refined central series & Connection between lower and upper central series

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Lower central series

GeneratedDerived subgroupSymmetric groupHall 1959Ordinal numbers
12 related topics

Refined central series

P-groupsElementary abelian groupsExponentFrattini subgroupSocle
9 related topics

Connection between lower and upper central series

Cyclic groupQuaternion groupDirect productPerfectCenterless
6 related topics

Definition

CentralCommutator subgroupFlagAdjoint actionEngel's theorem
5 related topics

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Overview

Definition

Lower central series

Upper central series

Connection between lower and upper central series

Refined central series

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Central series

Nodes58
Edges57
Triples57
Avg. degree1.97
Density0.034483
Components1

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Central series

Top relations

related to References · 34
Central series → American Mathematical Society, Assoc, Ellis, Eugene, Generalized, Glasgow Math, Graham, Group, ISBN, JSTOR, Krieger Publishing, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Lower Central Series, Macmillan, Marshall, Mat, MR, New Series
related to Connection between lower and upper central series · 8
Central series → C2, Ellis, For, However, LCS, Q8, There, UCS
related to Refined central series · 6
Central series → An, Frattini, In, Phi, The, There
related to Definition · 4
Central series → As, G/, Since, Thus
is a · 2
Central series → kind of normal series of subgroups or Lie subalgebras, sequence of subgroups
related to Lower central series · 1
Central series → The
related to Upper central series · 1
Central series → The
see also · 1
Central series → Nilpotent

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Important terminology

central series group subgroup nilpotent displaystyle upper lower groups called lcs ucs theory trivial center normal lie subgroups commutator solvable

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Central seriesis akind of normal series of subgroups or Lie subalgebras0.90text
Central seriesis asequence of subgroups0.90text
Central seriesrelated to Connection between lower and upper central seriesThere0.60section
Central seriesrelated to Connection between lower and upper central seriesLCS0.60section
Central seriesrelated to Connection between lower and upper central seriesUCS0.60section
Central seriesrelated to Connection between lower and upper central seriesEllis0.60section
Central seriesrelated to Connection between lower and upper central seriesFor0.60section
Central seriesrelated to Connection between lower and upper central seriesHowever0.60section
Central seriesrelated to Connection between lower and upper central seriesC20.60section
Central seriesrelated to Connection between lower and upper central seriesQ80.60section
Central seriesrelated to DefinitionSince0.60section
Central seriesrelated to DefinitionThus0.60section

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