Let : ZxZ→→ Z defined by o(a, b) = a - b.(a) Show that is a homomorphism.(b) Compute Ker and +(2xz)(c) Using FIT, to what known group is (Z x Z)/Ker o isomorphic to?

Let ϕ:ℤ×ℤ→ℤ defined by ϕa, b=a-b. (a) Show that ϕ is a homomorphism. Let a, b, c, d∈ℤ×ℤ…

Answered: Let ZxZ→ Z defined by (a, b) = a - b.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 28E

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Let ZxZ→ Z defined by (a, b) = a - b. (a) Show that is a homomorphism. (b) Compute Ker and +(2xz) (c) Using FIT, to what known group is (Z x Z)/Ker o isomorphic to?