1. Let (G, *) and (H, *) be groups. The direct product of G and H is the set G x H equipped with productgiven by(91, h1) · (92, h2) = (91 * 92, h1 * h2).c. Determine the order of an element (g, h) € G × H.d. Prove that G x H = H × G.

Answered: Image /qna-images/answer/96ec4872-81fb-488d-9fc0-6293be6813fc.jpg

Answered: 1. Let (G, *) and (H, *) be groups. The…

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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1. Let (G, *) and (H, *) be groups. The direct product of G and H is the set G x H equipped with product given by (91, h1) · (92, h2) = (gı * 92, hị * ha). c. Determine the order of an element (g, h) e G x H. d. Prove that G × H = H × G.

1. Let (G, ) and (H, ) be groups. The direct product of G and H is the set G x H equipped with product given by (91, h1) · (92, h2) = (gı * 92, hị * ha). c. Determine the order of an element (g, h) e G x H. d. Prove that G × H = H × G.