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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.

Advanced Engineering Mathematics
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) = (91 * 92, h1 * h2). c. Determine the order of an element (g, h) € G × H. d. Prove that G x H = H × G.
Transcribed Image Text: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) = (91 * 92, h1 * h2). c. Determine the order of an element (g, h) € G × H. d. Prove that G x H = H × G.
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