QI// Let (H, *) be a normal subgroup of the group (G, *) and we define: G/H={a*H: a € G} and we define on G/H by: (a*H) ® (b*H)=a*b)*H. Prove that (G/H, ® ) is a group.

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ZAIN IQ l.
زمر ثاني مسائي شهر 11. . .
امتحان زمر ۲ الشهر ۲ المرحلة الثانية مسائي. ۲۰۲۰-۲۰۲
QI// Let (H, *) be a normal subgroup of the group (G, *) and we
define:
G/H={a*H: a E G} and we define O on G/H by:
(a*H) ® (b*H)=(a*b)*H. Prove that (G/H, ® ) is a group.
Q2// Let (H, *) be a subgroup of the group (G, *). Prove that
(a*H)N(b*H)=0 or (a*H)=(b*H) for each a, b E G.
Transcribed Image Text:ZAIN IQ l. زمر ثاني مسائي شهر 11. . . امتحان زمر ۲ الشهر ۲ المرحلة الثانية مسائي. ۲۰۲۰-۲۰۲ QI// Let (H, *) be a normal subgroup of the group (G, *) and we define: G/H={a*H: a E G} and we define O on G/H by: (a*H) ® (b*H)=(a*b)*H. Prove that (G/H, ® ) is a group. Q2// Let (H, *) be a subgroup of the group (G, *). Prove that (a*H)N(b*H)=0 or (a*H)=(b*H) for each a, b E G.
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