p-primary component

Definition 1.

Let $G$ be a finite abelian group and let $p\mathrm{\in }\mathrm{N}$ be a prime. The $p$-primary component of $G$, ${\mathrm{\Pi }}_p$, 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
Canonical name	PprimaryComponent
Date of creation	2013-03-22 13:52:05
Last modified on	2013-03-22 13:52:05
Owner	alozano (2414)
Last modified by	alozano (2414)
Numerical id	5
Author	alozano (2414)
Entry type	Definition
Classification	msc 20D20
Synonym	primary component
Related topic	SylowPSubgroup