# a nontrivial normal subgroup of a finite $p$-group $G$ and the center of $G$ have nontrivial intersection

Let $G$ be a finite $p$-group, and let $H$ be a nontrivial normal subgroup^{} of $G$. Then $H\cap Z(G)\ne \{1\}$.

Title | a nontrivial normal subgroup of a finite $p$-group $G$ and the center of $G$ have nontrivial intersection^{} |
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Canonical name | ANontrivialNormalSubgroupOfAFinitePgroupGAndTheCenterOfGHaveNontrivialIntersection |

Date of creation | 2013-03-22 14:21:05 |

Last modified on | 2013-03-22 14:21:05 |

Owner | gumau (3545) |

Last modified by | gumau (3545) |

Numerical id | 4 |

Author | gumau (3545) |

Entry type | Theorem |

Classification | msc 20D20 |