# Tagged Questions

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### Finitely generated subgroups are cyclic, and a generalization

Is there a name for groups $G$ which satisfy the property that for any $a$ and $b$ in $G$, there is a $c\in G$ and integers $n$ and $m$ such that $a=c^n$ and $b=c^m$? Such a group has to be abelian, ...

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### Fibered products of cyclic groups

Background
Let $m,n$ be positive integers and consider the cyclic group $\mathbb{Z}_{mn}$.
We have a natural epimorphism $\mathbb{Z}_{mn} \to \mathbb{Z}_n$ coming from the exact sequence
$$ 0 \to ...