# p-primary component

###### Definition 1.

Let $G$ be a finite abelian group and let $p\in\mathbb{N}$ be a prime. The $p$-primary component of $G$, $\Pi_{p}$, is the subgroup of all elements whose order is a power of $p$.

Note: The $p$-primary component of an abelian group $G$ coincides with the unique Sylow $p$-subgroup of $G$.

Title p-primary component PprimaryComponent 2013-03-22 13:52:05 2013-03-22 13:52:05 alozano (2414) alozano (2414) 5 alozano (2414) Definition msc 20D20 primary component SylowPSubgroup