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Quotient group

In the branch of mathematics known as group theory, a quotient group or factor group is a group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored out").

Examples, Properties & Overview

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Explore the main themes, entities and connections around Quotient group. Start with the topic map, then use the sections below for research and deeper semantic analysis.

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Topics to explore

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Overview

Definition and illustration

Motivation for the name "quotient"

Examples

Properties

Quotients of Lie groups

Advanced semantic analysis

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Map overview Semantic statistics

Quotient group

Nodes75
Edges74
Triples47
Avg. degree1.97
Density0.026667
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Quotient group

Top relations

related to Definition and illustration · 8
Quotient group → Cosets, For, G/H, Given, Na, The, Then, This
related to Real numbers modulo the integers · 8
Quotient group → Adding, An, Consider, Each, Euler's, Since, SO, The
related to Complex integer roots of 1 · 5
Quotient group → Consider, One, The, This, Thus
related to Definition · 5
Quotient group → As, It, Let, Since, The
related to Motivation for the name "quotient" · 5
Quotient group → Because, In, The, These, When
related to Even and odd integers · 4
Quotient group → Consider, Example, There, This
related to Example: Addition modulo 6 · 4
Quotient group → Consider, For, The, Then
related to Integer modular arithmetic · 4
Quotient group → Both, Consider, The, This
is a · 2
Quotient group → same idea, subgroup
related to Properties · 2
Quotient group → If, The

Important terminology Word statistics

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Important terminology

displaystyle group subgroup normal quotient cosets mathbb left isomorphic right operation integers modulo consider set elements addition mathrm one example

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Quotient groupis asubgroup0.90text
Quotient groupis asame idea0.90text
Quotient grouprelated to Complex integer roots of 1The0.60section
Quotient grouprelated to Complex integer roots of 1Consider0.60section
Quotient grouprelated to Complex integer roots of 1This0.60section
Quotient grouprelated to Complex integer roots of 1One0.60section
Quotient grouprelated to Complex integer roots of 1Thus0.60section
Quotient grouprelated to DefinitionLet0.60section
Quotient grouprelated to DefinitionThe0.60section
Quotient grouprelated to DefinitionIt0.60section
Quotient grouprelated to DefinitionAs0.60section
Quotient grouprelated to DefinitionSince0.60section

Related concept clusters Concept neighborhoods

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    Connections between topic areas Semantic bridges

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    Min side: 3
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