e 0:YA* ZAIN IQQI// Let (H, *) be a normal subgroup of the group (G, *) and wedefine:G/H={a*H: a € 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)=@ or (a*H)=(b*H) for each a, b € G.

Answered: Image /qna-images/answer/6ec9f150-ad5c-4474-8a14-201403e95e06.jpg

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

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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

e 0:YA
* ZAIN IQ
QI// Let (H, *) be a normal subgroup of the group (G, *) and we
define:
G/H={a*H: a € 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)=@ or (a*H)=(b*H) for each a, b € G.

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