(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If G is an Abelian group and contains cyclic subgroups of orders 4 and 6, what other sizes of cyclic subgroups must G contain?

2. Relevant equations

A cyclic group of order n has cyclic subgroups with orders corresponding to all of n's divisors.

3. The attempt at a solution

I know that a cyclic group of order n has cyclic subgroups with orders corresponding to all of n's divisors, so I'm inclined to say that G must have cyclic subgroups with orders 1, 2, and 3. But I also have a hunch that the subgroups of orders 4 and 6 combine in some way, so maybe there's also a cyclic subgroup of order lcm(4,6) = 12? Am I on the right track here?

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# Homework Help: Cyclic subgroups of an Abelian group

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