# 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 $H\cap Z(G)\neq\{1\}$.

Title a nontrivial normal subgroup of a finite $p$-group $G$ and the center of $G$ have nontrivial intersection ANontrivialNormalSubgroupOfAFinitePgroupGAndTheCenterOfGHaveNontrivialIntersection 2013-03-22 14:21:05 2013-03-22 14:21:05 gumau (3545) gumau (3545) 4 gumau (3545) Theorem msc 20D20