Questions:Normal subgroup

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This is a questions page on normal subgroup, listing common questions that may occur both to people encountering the definition for the first time and to people who have spent some time with the definition.

In addition to reading these questions, you should read: normal subgroup (the main page on the topic), nonstandard definitions of normal subgroup, proving normality, using normality, normal versus characteristic, ubiquity of normality.

Also see facts about normality, facts that prove that a subgroup is normal, and facts that use that a subgroup is normal.

 Question aboutQuestion typeAnswer references
Isomorphic normal subgroups isomorphic quotient groups equivalent as subgroupsNormal subgroup
Quotient map
Isomorphic groups
complete description conjectureSeries-equivalent not implies automorphic
Series-equivalent subgroups
Automorphic subgroups
Normal subgroup abelian group relationNormal subgroup
Abelian group
relation between two concepts
Normal subgroup center relationNormal subgroup
Center
relation between two concepts
Normal subgroup characteristic in bigger groupNormal subgroup
Characteristic subgroup
Normal subgroup characteristic subgroup invariance confusionNormal subgroup
Characteristic subgroup
relation between two concepts
confusion
Normal subgroup characteristic subgroup relationNormal subgroup
Characteristic subgroup
relation between two concepts
Normal subgroup definition inequality confusionNormal subgroupmultiple definitions
confusion
Normal subgroup direct productNormal subgroup
Direct factor
Internal direct product
External direct product
relation between two concepts
Normal subgroup endomorphismsNormal subgroup
Endomorphism of a group
relation between two concepts
Normal subgroup inner automorphism significanceNormal subgroup
Inner automorphism
relation between two concepts
significance
Normal subgroup multiple definitionsNormal subgroupmultiple definitions
overload
Normal subgroup of normal subgroup big dealNormal subgroup
Transitive subgroup property
significanceNormality is not transitive
2-subnormal subgroup
Subnormal subgroup
Third isomorphism theorem
Normal subgroup product with subgroupsNormal subgroup
Product of subgroups
Permutable subgroup
Normal implies permutable
Permutable not implies normal
Normal subgroup quotient group determine whole groupNormal subgroup
Quotient map
Isomorphic groups
complete description conjecture
Normal subgroup quotient group determine whole group counterfactualNormal subgroup
Quotient map
Isomorphic groups
counterfactual