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Conjugacy class

In mathematics, especially group theory, two elements a {\displaystyle a} and b {\displaystyle b} of a group are conjugate if there is an element g {\displaystyle g} in the group such that b = g a g − 1 . {\displaystyle b=gag^{-1}.} This is an equivalence relation whose equivalence classes are called conjugacy classes. In other words, each conjugacy…

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Overview

Motivation

Definition

Properties

Examples

Conjugation as a group action, centralizers, and the class equation

Conjugacy of subgroups and general subsets

Geometric interpretation

Conjugacy class and irreducible representations in finite group

Advanced semantic analysis

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Map overview Semantic statistics

Conjugacy class

Nodes65
Edges64
Triples30
Avg. degree1.97
Density0.030769
Components1

How this topic connects Entity context

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Conjugacy class

Top relations

related to Conjugacy of subgroups and general subsets · 7
Conjugacy class → As, By, Cl, Define, Let Cl, More, The
related to Conjugation as a group action, centralizers, and the class equation · 6
Conjugacy class → For, Let, Moreover, The, Then, This
related to Properties · 6
Conjugacy class → Cl, Hence, If, More, The, This
related to Conjugacy class equation · 4
Conjugacy class → For, Longleftrightarrow, This, Thus
related to Examples · 3
Conjugacy class → No, The, Transposing
is a · 1
Conjugacy class → set containing one element
related to Average centralizer · 1
Conjugacy class → By Burnside's
related to Conjugacy class and irreducible representations in finite group · 1
Conjugacy class → In
related to Geometric interpretation · 1
Conjugacy class → Conjugacy

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Important terminology

displaystyle conjugacy group class operatorname elements -1 classes element conjugate two order subsets number one gag cl example subgroups centralizer

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Conjugacy classis aset containing one element0.90text
Conjugacy classrelated to Average centralizerBy Burnside's0.60section
Conjugacy classrelated to Conjugacy class and irreducible representations in finite groupIn0.60section
Conjugacy classrelated to Conjugacy class equationFor0.60section
Conjugacy classrelated to Conjugacy class equationThis0.60section
Conjugacy classrelated to Conjugacy class equationLongleftrightarrow0.60section
Conjugacy classrelated to Conjugacy class equationThus0.60section
Conjugacy classrelated to Conjugacy of subgroups and general subsetsMore0.60section
Conjugacy classrelated to Conjugacy of subgroups and general subsetsLet Cl0.60section
Conjugacy classrelated to Conjugacy of subgroups and general subsetsCl0.60section
Conjugacy classrelated to Conjugacy of subgroups and general subsetsDefine0.60section
Conjugacy classrelated to Conjugacy of subgroups and general subsetsThe0.60section

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