Chapter 2, exercise 5.1: Let : G → G' be a surjective homomorphism. Prove that if G is cyclic, then G' is cyclic, and if G is abelian, then G' is abelian.
Chapter 2, exercise 5.1: Let : G → G' be a surjective homomorphism. Prove that if G is cyclic, then G' is cyclic, and if G is abelian, then G' is abelian.
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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![(1) Chapter 2, exercise 5.1: Let y: G → G' be a surjective homomorphism. Prove that
if G is cyclic, then G' is cyclic, and if G is abelian, then G' is abelian.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed3eef2a-70e8-485e-b91d-563de65921b3%2F53bf9789-063d-408b-8e63-e8a08bfc31ea%2Fcdn1xxh_processed.png&w=3840&q=75)
Transcribed Image Text:(1) Chapter 2, exercise 5.1: Let y: G → G' be a surjective homomorphism. Prove that
if G is cyclic, then G' is cyclic, and if G is abelian, then G' is abelian.
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