**Question 2:**Prove that $ \mathbb{Z}_m \times \mathbb{Z}_n $ is a cyclic group if and only if $ \gcd(m, n) = 1 $. Find all generators of cyclic group $ \mathbb{Z}_5 \times \mathbb{Z}_4 $.

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2) Prove that Zm × Zn is a cyclic group if and only if gcd(m, n) cyclic group Z; x Z4. = 1. Find all generators of

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 11E: Find all homomorphic images of the quaternion group.

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