p-primary component

Definition 1.

Let G be a finite abelian group and let pN be a prime. The p-primary componentPlanetmathPlanetmath of G, Πp, is the subgroupMathworldPlanetmathPlanetmath of all elements whose order is a power of p.

Note: The p-primary component of an abelian groupMathworldPlanetmath 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