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For every integer r≥ 1 let C, denote the cyclic group {e²rik/r: 0≤k

For every integer r≥ 1 let C, denote the cyclic group {e²rik/r: 0≤k

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 30E: Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are...
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For every integer r≥ 1 let C, denote the cyclic group {e²rik/r: 0≤k <r} < Cx. Let n, n ≥ 1 be a pair of integers whose highest common factor is 1. Define a function : Cn x Cm → Cnm by (e²nik/n, ²nil/m) := ²nik/n. 2πil/m Prove that is an isomorphism.
Transcribed Image Text:For every integer r≥ 1 let C, denote the cyclic group {e²rik/r: 0≤k <r} < Cx. Let n, n ≥ 1 be a pair of integers whose highest common factor is 1. Define a function : Cn x Cm → Cnm by (e²nik/n, ²nil/m) := ²nik/n. 2πil/m Prove that is an isomorphism.
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