Group Theory – Building abelian groups

I propose to find all the abelian groups up to order 100. It’s pretty easy, and there’s one nice idea that will simplify things. An abelian group, I hope you recall, is one that is commutative.

(The smallest non-abelian group is D3, the dihedral group of order 6… which is isomorphic to S3, the symmetric group on 3 symbols. All other dihedral groups are non-abelian, and the quaternion group of order 8 is non-abelian. But we’re going to look for abelian groups.)
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