/sci/ - Science & Math

>>9046037
So we have [math]\varphi(gh'g^{-1}) = hh'h^{-1}[/math] for some [math]h \in H[/math]. So sure, [math]\varphi(gh'g^{-1}) \in H[/math], but we already knew that. Why does considering this tell us anything about [math]gh'g^{-1}[/math] being in [math]H[/math]?

>>9046029
Is it? Artin's proof uses the normality of both (pic related).