Question

(b) Show that KHK' is onto if and only if every subgroup of G is closed. 10. Let E2F be fields with G = gal(E:F). If HCG is a subgroup and H is finite, show that H is closed. 11. If FDK Fare fields show that Ke Aalnie if and anku. K le clnced ne an

#10.] Let $E\supseteq F$ be fields with $G=gal(E:F)$ . If $H\subseteq G$ is a subgroup and $H^{\circ}{}'$ is finite, show that is closed.

Answer 1

Ans:) Given,

G = gal E:F)
. If
HCG
is a subgroup and $H^{\circ}{}'$ is finite.

Anos - Given fi R² M df (1,0) = (1, 4,59 df Co, D.p = (3, 7, 004 fr = n² de dy fn ( (2,0p, 10, 3p) = 2 de (2,0). A dy (0, 3e = x2 (2.90 (922,00 pou n (C2.8, 10), (1,2,)q) - dx (210) A dy (0,3).

Anos - Given fi R² M df (1,0) = (1, 4,59 df Co, D.p = (3, 7, 004 fr = n² de dy fn ( (2,0p, 10, 3p) = 2 de (2,0). A dy (0, 3e = x2 (2.90 (922,00 pou n (C2.8, 10), (1,2,)q) - dx (210) A dy (0,3).