A subgroup N of G is normal if g^{-1}Ng = N for all g in G.
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Replying to @AlgebraFact
The way I like to think of this is that normal subgroups don't "mix" with the rest of the group when conjugated. For example, in the Euclidean group, translations are a normal subgroup while orthogonal transformations are not.
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Replying to @DavidRoomeAuth @AlgebraFact
Yea I think of it as being closed under the group action
11:04 AM - 26 Dec 2019
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