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Let m, n ɛ Z+ such that gcd(m, n) = 1. Suppose there are M and N abelian groups, up to isomorphism, of order m and n, respectively. Show that there are MN abelian of order mn. groups

Let m, n ɛ Z+ such that gcd(m, n) = 1. Suppose there are M and N abelian groups, up to isomorphism, of order m and n, respectively. Show that there are MN abelian of order mn. groups

Advanced Engineering Mathematics
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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Let m, n e Zt such that gcd(m, n) = 1. Suppose there are M and N abelian groups, up to isomorphism, of order m and n, respectively. Show that there are MN abelian groups of order mn. %3D
Transcribed Image Text:Let m, n e Zt such that gcd(m, n) = 1. Suppose there are M and N abelian groups, up to isomorphism, of order m and n, respectively. Show that there are MN abelian groups of order mn. %3D
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