Suppose that f: G - G such that f(x) = axa². Then fis a group homomorphism ifand only ifa^3 = ea = eO a^4 = ea^2 = e

f:G→G such that fx=axa2 We know that f is a homomorphism if fxy=fxfy for all x, y∈G

Answered: Suppose that f:G - G such that f(x) =…

Suppose that f:G - G such that f(x) = axa". Then fis a group homomorphism if and only if O a^3 = e a = e O a^4 = e a^2 = e O O O

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 11E: 11. Show that defined by is not a homomorphism.

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Question

Suppose that f: G - G such that f(x) = axa². Then fis a group homomorphism if
and only if
a^3 = e
a = e
O a^4 = e
a^2 = e

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