10(2)Consider the two multiplicative groups (R.) and (R.)and let f: (R.) → (R,) be a map defined byf(x) = x²for all x E R.(a) Show that f is a group homomorphism.(b) Compute kerf.(c) Is f one-to-one? Justify your answer.(d) Is f onto? Justify your answer.(e) Is f an isomorphism? Justify your answer.(f) Show that R*/{-1,1} = R.

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Answered: Consider the two multiplicative groups…

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 32E: 32. Let be a fixed element of the group . According to Exercise 20 of section 3.5, the mapping ...

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