Prüfer group
In mathematics, specifically in group theory, the Prüfer p-group or the p-quasicyclic group or p ∞ {\displaystyle p^{\infty }} -group, Z ( p ∞ ) {\displaystyle \mathbb {Z} (p^{\infty })} , for a prime number p is the unique p-group in which every element has p different p-th roots. The Prüfer p-groups are countable abelian groups that are important in the classification of infinite abelian groups: they (along with the group of rational numbers) form the smallest building blocks of all divisible groups.