a. Let n,m in Z>0. Prove: (Z/nZ) x (Z/mZ) isomorphic to (Z/lcm(n,m)Z) x (Z/gcd(n,m)Z). Hint: you can use the following property: let n1, n2 ... nt be positive whole numbers, such that for all indices i !=j gcd(ni, nj) = 1. Let N = n1 * n2 .. * nt, then Z/NZ isomorphic to (Z/n1Z) x (Z/n2Z) ... x (Z/ntZ). b. Give an explicit isomorphism between Z/4Z x Z/6Z -> Z/12Z x Z/2Z

a. Let n,m in Z>0. Prove: (Z/nZ) x (Z/mZ) isomorphic to (Z/lcm(n,m)Z) x (Z/gcd(n,m)Z). Hint: you can use the following property: let n1, n2 ... nt be positive whole numbers, such that for all indices i !=j gcd(ni, nj) = 1. Let N = n1 * n2 .. * nt, then Z/NZ isomorphic to (Z/n1Z) x (Z/n2Z) ... x (Z/ntZ). b. Give an explicit isomorphism between Z/4Z x Z/6Z -> Z/12Z x Z/2Z

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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