Answered: Let G and G' be groups. (a) If p: G →…

Let G and G' be groups. (a) If p: G → G' is a function, what is required for p to be a homomorphism? (b) Prove that if p : G → G' is an injective homomorphism and a e G, then |p(a)| = |a| %3D

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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Question

Let G and G' be groups.
(a) If p: G → G' is a function, what is required for p to be a homomorphism?
(b) Prove that if p : G → G' is an injective homomorphism and a e G, then |p(a)| = |a|
%3D

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