nLab prime power



In the natural numbers, a prime power p np^n is a positive power n1n \geq 1 of a prime number pp.


The fundamental theorem of arithmetic states that every positive natural number is a finite product of prime powers.

Uses in other parts of mathematics

In group theory, a group is a p-primary group if its order is a prime power of the given prime number pp.

The fundamental theorem of finite abelian groups states that every finite abelian group is the direct sum of cyclic groups of prime power order.

In ring theory, the integers modulo n which are local rings are precisely the integers modulo a prime power.

See also

Created on December 8, 2022 at 22:46:00. See the history of this page for a list of all contributions to it.