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.

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Let m, n E 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 groups of order mn.
Transcribed Image Text:Let m, n E 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 groups of order mn.
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