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A [[subgroup]] ''N'' of a [[Group (mathematics)|group]] ''G'' is a '''normal subgroup''', if one of the following equivalent conditions holds:
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>