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, 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.
Alexander SkopinBrunnian linkCarter subgroupCenter (group theory)Commutator collecting processCommutator subgroupDescendant tree (group theory)Engel's theoremFitting lengthFocal subgroup theoremFree Lie algebraFree groupGraded Lie algebraGromov's theorem on groups of polynomial growthHall wordHypercenterHypercentral groupHypocentral groupJennings seriesLie algebraLower Central SeriesLower central seriesNilmanifoldNilpotent Lie algebraNilpotent groupNilpotent residualNilpotent spaceNorm (group)P-groupParafree groupPerfect groupPower automorphismPowerful p-groupProjective linear groupProjective orthogonal groupSubgroup seriesThree subgroups lemmaUnipotentUpper Central SeriesUpper central series
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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, 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.
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In mathematics, especially in ...... only if a group is nilpotent.
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Soit G un groupe, au sens math ...... est dit nilpotent de classe n.
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In mathematics, especially in ...... rms are used for Lie algebras.
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Soit G un groupe, au sens math ...... nt à la relation d'inclusion).
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Central series
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Suite centrale descendante
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