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
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