Suppose that f: G - G such that f(x) = axa. Then fis a group homomorphism ifand only if) a^4 = e%3DO a^3 = ea^2 = ea = eThe set of all even integers 2Z is asubgroup of (Z, +) Then the right coset-5 + 2Z contains the elementO 74O 10

(1) It is given that the function is fx=axa2. For homomorphism, the function follows the condition…

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 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 * 7 4 10

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 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 * 7 4 10

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 - G such that f(x) = axa. Then fis a group homomorphism if
and only if
) a^4 = e
%3D
O a^3 = e
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
4
O 10

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