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p-primary component (Definition)
Definition 1   Let $G$ be a finite abelian group and let $p\in \Nats$ 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 $G$




"p-primary component" is owned by alozano.
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See Also: Sylow p-subgroup

Other names:  primary component
Keywords:  primary component
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Cross-references: power, order, subgroup, component, prime, abelian group, finite

This is version 2 of p-primary component, born on 2003-08-18, modified 2003-08-18.
Object id is 4610, canonical name is PPrimaryComponent.
Accessed 3614 times total.

Classification:
AMS MSC20D20 (Group theory and generalizations :: Abstract finite groups :: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure)

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