 Prüfer group

For a prime $p$, the Prüfer group $C_{p^{\infty }}$ is the union of an ascending chain of cyclic groups of orders $p,p^2,p^3,\dots$. As a $\mathbb{Z}$-module it is Artinian but not Noetherian.

A Prüfer group, also known as a Prüfer \(p\)-group, is a type of abelian group that can be defined for a prime number \(p\).