Well, I have a little doubt. If $G_1$ and $G_2$ are free groups in $H_1$ and $H_2$ respectively. If we have $\langle x^2 : x \in G_1 \rangle = K_1 \lhd G_1$ and $\langle y^2 : y \in G_2 \rangle = K_2 \lhd G_2$. We can conclude that: if $G_1 \cong G_2$, then $G_1/K_1 \cong G_2/K_2$? If so, could you give me any tips on where to start?
2026-03-29 18:33:32.1774809212
Isomorphism of quotient groups: if $G_1 \cong G_2$, then $G_1/K_1 \cong G_2/K_2$?
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