Solve correctlyASAPDo both parts 4. Consider the following groups G and H, K < G. If G is isomorphic toH × K, give an isomorphism y : G → H × K. If not, say why G andH × K cannot be isomorphic.(a) G = R*, H = {1, –1}, K = R+(b) G = D4, H = {1,r, r², r³}, K = {1, s}%3D

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Answered: 1. Consider the following groups G and…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 2E: Let G1, G2, and G3 be groups. Prove that if 1 is an isomorphism from G1 to G2 and 2 is an...

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1. Consider the following groups G and H, K < G. If G is isomorphic to H × K, give an isomorphism v : G → H × K. If not, say why G and H × K cannot be isomorphic. (a) G = R*, H = {1,–1}, K = R+ (b) G = D4, H = {1,r, r² , r³}, K = {1, s}