Answered: Let G and H be groups and consider the…

Let G and H be groups and consider the function f: G → G × H defined by f(g) = (g, eH ) where eH is the identity of H. How do you prove that f is a group homomorphism?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 28E

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Let G and H be groups and consider the function f: G → G × H defined by f(g) = (g, eH ) where eH is the identity of H. How do you prove that f is a group homomorphism?

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