# Math Help - showing center of a group is normal

1. ## showing center of a group is normal

Show that the center of a group is normal...

2. Originally Posted by szpengchao
Show that the center of a group is normal...
$H\triangleleft G$ if and only if $ghg^{-1} \in H$ for all $h\in H$ and $g\in G$.
Using this definition it should be a straightforward proof.