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Normal subgroup

In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup N {\displaystyle N} of the group G {\displaystyle G} is normal in G {\displaystyle G} if and only if g n g − 1 ∈ N…

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Overview

Definitions

Examples

Properties

Normal subgroups, quotient groups and homomorphisms

Operations taking subgroups to subgroups

Subgroup properties complementary (or opposite) to normality

Subgroup properties stronger than normality

Subgroup properties weaker than normality

Related notions in algebra

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Map overview Semantic statistics

Normal subgroup

Nodes89
Edges88
Triples55
Avg. degree1.98
Density0.022472
Components1

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Normal subgroup

Top relations

related to External links · 12
Normal subgroup → Abstract Algebra, Baez, Eric, Gowers, Group Fundamentals, MathematicsRobert Ash, MathWorld, Normal, Springer's Encyclopedia, The Basic Graduate YearTimothy, Weisstein, What's
related to Equivalent conditions · 10
Normal subgroup → Any, For, G/N, Multiplication, Ng, That, The, There, Therefore, This
related to Properties · 10
Normal subgroup → Every, For, However, If, In, More, Normality, T-group, That, The
related to Examples · 8
Normal subgroup → For, Hamiltonian, If, In, Likewise, More, Ng, Other
related to Normal subgroups, quotient groups and homomorphisms · 8
Normal subgroup → G/N, If, It, Then, There, This, To, With
related to Lattice of normal subgroups · 3
Normal subgroup → Given, NM, The
is a · 1
Normal subgroup → subgroup N
related to Definitions · 1
Normal subgroup → The
related to Subgroup properties complementary (or opposite) to normality · 1
Normal subgroup → Malnormal
related to Subgroup properties weaker than normality · 1
Normal subgroup → Subnormal

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Important terminology

displaystyle normal subgroup group subgroups homomorphism conjugation quotient element two -1 relation cosets also every normality groups homomorphisms index product

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Normal subgroupis asubgroup N0.90text
Normal subgrouprelated to DefinitionsThe0.60section
Normal subgrouprelated to Equivalent conditionsFor0.60section
Normal subgrouprelated to Equivalent conditionsTherefore0.60section
Normal subgrouprelated to Equivalent conditionsThe0.60section
Normal subgrouprelated to Equivalent conditionsNg0.60section
Normal subgrouprelated to Equivalent conditionsMultiplication0.60section
Normal subgrouprelated to Equivalent conditionsThat0.60section
Normal subgrouprelated to Equivalent conditionsThere0.60section
Normal subgrouprelated to Equivalent conditionsThis0.60section
Normal subgrouprelated to Equivalent conditionsG/N0.60section
Normal subgrouprelated to Equivalent conditionsAny0.60section

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