14. If G is abelian and p: G→ G' is a homomorphism of G onto G', provethat G' is abelian.

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Answered: 14. If G is abelian and p: G→ G' is a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 18E: Let a and b be elements of a group G. Prove that G is abelian if and only if (ab)2=a2b2.

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14. If G is abelian and p: G→ G' is a homomorphism of G onto G', prove that G' is abelian.