10. Let H be a group under addition and define q : Z → H by q(n) = n · (mod 4). a.) Prove that is a homomorphism of the additive group Z and H. b.) What is the ker(p)? c.) Use the 1st isomorphism theorem to determine the isomorphism type of q(Z) ? ` `In other words, to which well known group is o(Z) isomorphic to?

10. Let H be a group under addition and define q : Z → H by q(n) = n · (mod 4). a.) Prove that is a homomorphism of the additive group Z and H. b.) What is the ker(p)? c.) Use the 1st isomorphism theorem to determine the isomorphism type of q(Z) ? ` `In other words, to which well known group is o(Z) isomorphic to?

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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