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.

We have M and N are abelian groups of order m and n. so, we know that MN is abelian group.

Answered: Let m, n e Zt such that gcd(m, n) = 1.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 18E

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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.