A subgroup N of G is normal if g^{-1}Ng = N for all g in G.
As long as we’re using that notation we can write it more compactly as GNG^{-1}=N
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Tbh if we're being pedantic I would interpret that notation to range over all possible products g_1ng_2^{-1} which is not what we want here... the former notation gets at what we really want a little more precisely
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Good thing you’re not allowed to be pedantic in math
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New conversation -
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Might we not interpret that as "for all n there exists g and g' and n' such that gn'g'^(-1)=n'?
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