Suppose that f: G goes to G such that f(x) = a x a². Then f is a group homomorphism if and only if :a⁴ =e, a³=e, a²=e or a=e Suppose that f:G G such that f(x) = axa?. Then f is a group homomorphism ifand only ifO a*4 = eO a*3 = e() a*2 = eO a= eREDMI NOTE 9SAl QUAD CAMERA

Answered: Image /qna-images/answer/9ee1b77f-7b7f-4d8b-bad1-a91213f4caa7.jpg

Suppose that f: G and only if → G such that f(x) = axa?. Then f is a group homomorphism if O a^4 = e O a*3 = e O a*2 = e a = e REDMI NOTE 9S O AI QUAD CAMERA

Suppose that f: G and only if → G such that f(x) = axa?. Then f is a group homomorphism if O a^4 = e O a3 = e O a2 = e a = e REDMI NOTE 9S O AI QUAD CAMERA

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 27E: 27. a. Show that a cyclic group of order has a cyclic group of order as a homomorphic image. ...

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Question

Suppose that f: G goes to G such that f(x) = a x a². Then f is a group homomorphism if and only if : a⁴ =e, a³=e, a²=e or a=e

Suppose that f:G G such that f(x) = axa?. Then f is a group homomorphism if
and only if
O a*4 = e
O a*3 = e
() a*2 = e
O a= e
REDMI NOTE 9S
Al QUAD CAMERA

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