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

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 9E: 9. Suppose that and are subgroups of the abelian group such that . Prove that .

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Question

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

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