Normal subgroup

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A subgroup N of a group G is a normal subgroup, if one of the following equivalent conditions holds:

  1. <math>a N = N a </math> for all <math> a \in G</math>
  2. <math>a N a^{-1} \subset N </math> for all <math> a \in G</math>
  3. <math>a N a^{-1} = N </math> for all <math> a \in G</math>
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