# 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 |