1. Let (G, +) and (H,*) be groups. The direct product of G and H is the set G × H equipped with product given by (91, h3) · (92, h2) = (91 * 92, h1 * h2). a. Verify that the direct product (G × H,') is a group. b. Prove that G x H is abelian if ar elian.
1. Let (G, +) and (H,*) be groups. The direct product of G and H is the set G × H equipped with product given by (91, h3) · (92, h2) = (91 * 92, h1 * h2). a. Verify that the direct product (G × H,') is a group. b. Prove that G x H is abelian if ar elian.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 33E: Suppose that G and H are isomorphic groups. Prove that G is abelian if and only if H is abelian.
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