- #1
SMA_01
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Homework Statement
Let m and n be relatively prime positive integers. Show that if there are, up to isomorphism, r abelian groups of order m and s of order n, then there are rs abelian groups of order mn.
Homework Equations
The Attempt at a Solution
I'm not sure how to go about this. I was thinking of saying that since m and n are relatively prime, the gcd(m,n)=1; wouldn't this then imply that the group order would be mn? Because mn is the lcm of m and n?
Any help is appreciated.