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Composition series

In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many naturally occurring modules are not semisimple, hence cannot be decomposed into a direct sum of simple modules. A…

For groups, Overview & For objects in an abelian category

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For groups

13 related topics

Overview

18 related topics

For objects in an abelian category

6 related topics

For modules

2 related topics

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Overview

For groups

For modules

Generalization

For objects in an abelian category

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Composition series

Nodes47
Edges46
Triples41
Avg. degree1.96
Density0.042553
Components1

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Composition series

Top relations

related to Generalization · 11
Composition series → An, Attention, Bourbaki, Ch, Groups, Hölder, Isaacs, Jordan, Module, The, Thus
related to Uniqueness: Jordan–Hölder theorem · 11
Composition series → Baumslag, Birkhoff, Camille Jordan, However, Hölder, Jordan, Otto Hölder, Schreier, That, The Jordan, This
related to For modules · 8
Composition series → As, Given, Hölder, In, Jk, Jordan, R-module, The
related to For groups · 4
Composition series → G/N, If, More, Otherwise
see also · 3
Composition series → Krohn, Rhodes, Schreier Refinement Theorem
is a · 2
Composition series → maximal subnormal series, subnormal series such that each factor group Hi
related to For objects in an abelian category · 2
Composition series → If, Xi

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Important terminology

composition series group simple theorem finite jordan hölder groups modules subnormal module may length maximal submodules factors algebra normal pieces

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Composition seriesis amaximal subnormal series0.90text
Composition seriesis asubnormal series such that each factor group Hi0.90text
Composition seriesrelated to For groupsIf0.60section
Composition seriesrelated to For groupsG/N0.60section
Composition seriesrelated to For groupsOtherwise0.60section
Composition seriesrelated to For groupsMore0.60section
Composition seriesrelated to For modulesThe0.60section
Composition seriesrelated to For modulesGiven0.60section
Composition seriesrelated to For modulesR-module0.60section
Composition seriesrelated to For modulesJk0.60section
Composition seriesrelated to For modulesAs0.60section
Composition seriesrelated to For modulesIn0.60section

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    Min side: 3
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