Difference between revisions of "Normal subgroup"
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| − | A [[subgroup]] ''N'' of a [[Group (mathematics)|group]] ''G'' is a '''normal subgroup''' | + | A [[subgroup]] ''N'' of a [[Group (mathematics)|group]] ''G'' is a '''normal subgroup''' (written <math>N \triangleleft G</math>) if one of the following equivalent conditions holds: |
# <math>a N = N a </math> for all <math> a \in G</math> | # <math>a N = N a </math> for all <math> a \in G</math> | ||
Latest revision as of 02:36, December 18, 2008
A subgroup N of a group G is a normal subgroup (written <math>N \triangleleft G</math>) if one of the following equivalent conditions holds:
- <math>a N = N a </math> for all <math> a \in G</math>
- <math>a N a^{-1} \subset N </math> for all <math> a \in G</math>
- <math>a N a^{-1} = N </math> for all <math> a \in G</math>