*Suppose that f:G → G such that f(x) = axa. Then fis a group homomorphism ifand only ifa^4 = eO a^3 = eO a^2 = ea = eThe set of all even integers 2Z is asubgroup of (Z, +) Then the right coset-5 + 2Z contains the element *O 7О 4О 10

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 a^4 = e a^3 = e O a^2 = e O a = e

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 36E

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Question

*
Suppose that f:G → G such that f(x) = axa. Then fis a group homomorphism if
and only if
a^4 = e
O a^3 = e
O a^2 = e
a = e
The set of all even integers 2Z is a
subgroup of (Z, +) Then the right coset
-5 + 2Z contains the element *
O 7
О 4
О 10

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