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Simple group

In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, namely a nontrivial normal subgroup and the corresponding quotient group. This process can be repeated, and for finite groups one eventually arrives at uniquely…

History, History for finite simple groups & Examples

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Overview

Examples

Finite simple groups

Classification

Structure of finite simple groups

History for finite simple groups

Tests for nonsimplicity

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Map overview Semantic statistics

Simple group

Nodes79
Edges78
Triples66
Avg. degree1.97
Density0.025316
Components1

How this topic connects Entity context

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Simple group

Top relations

related to Finite simple groups · 13
Simple group → Briefly, Daniel Gorenstein, Hölder, If, In, Jordan, On, One, PSL, Similarly, Since, The, This
related to Infinite simple groups · 11
Simple group → Another, Burger, Explicit, Finitely, Graham Higman, Higman, It, Mozes, The, This, Thompson
related to Classification · 10
Simple group → Daniel Gorenstein, Feit, Monster, One, Soon, Tarski, The, There, This, Thompson
related to Construction · 8
Simple group → Camille Jordan, Chevalier, Galois, Jordan, PSL, Simple, The, This
related to Tests for nonsimplicity · 7
Simple group → If, Let, Proof, Since, Sylow, Sylow's, Sylow's Third Theorem
related to history · 6
Simple group → By, Galois, Monster, See, Silvestri, There
related to Structure of finite simple groups · 6
Simple group → Feit, The, The Schreier, Therefore, This, Thompson
is a · 3
Simple group → alternating group A 5, nontrivial group whose only normal subgroups are the trivial group and the group itself, projective special linear group PSL
see also · 2
Simple group → Almost, List

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Important terminology

simple groups group finite order prime displaystyle classification theorem one infinite since every monster subgroup normal mathematics cyclic lie type

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Simple groupis anontrivial group whose only normal subgroups are the trivial group and the group itself0.90text
Simple groupis aalternating group A 50.90text
Simple groupis aprojective special linear group PSL0.90text
Simple grouprelated to ClassificationThere0.60section
Simple grouprelated to ClassificationOne0.60section
Simple grouprelated to ClassificationTarski0.60section
Simple grouprelated to ClassificationThe0.60section
Simple grouprelated to ClassificationFeit0.60section
Simple grouprelated to ClassificationThompson0.60section
Simple grouprelated to ClassificationSoon0.60section
Simple grouprelated to ClassificationMonster0.60section
Simple grouprelated to ClassificationDaniel Gorenstein0.60section

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