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.

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.

单词	Quasicyclic group
释义	Quasicyclic group 英语百科 Prüfer group （重定向自Quasicyclic group） 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.
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