Let ø : Z25 → S8 be a homomorphism such that ø(1) = (12468).(a) Find ø(22).(b) Determine kerø.(c) Show that Z25/kerø = Z5.

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Answered: Let ø: Z25 → S8 be a homomorphism such…

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 14E: 14. Let be an abelian group of order where and are relatively prime. If and , prove that .

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Let ø: Z25 → S8 be a homomorphism such that o(1) = (12468). (a) Find ø(22). (b) Determine kerø. (c) Show that Z25/kerø = Z5.