Prüfer group
（重定向自Quasicyclic group）
![The Prüfer 2-group with presentation <gn: gn+12 = gn, g12 = e>, illustrated as a subgroup of the unit circle in the complex plane.](/Images/godic/202502/05/Prüfer3341.png")
In mathematics, specifically in group theory, the Prüfer p-group or the p-quasicyclic group or p-group, Z(p), 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 which 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.