Yesterday i heard that a connected Lie group $G$ is simply connected (i.e. $\pi\_1(G)=0$) if and only if $G$ is simple as a group, i.e. $G$ has no nontrivial normal subgroup. That sounds too good to be wrong, it explains why one would call this property "simply connectedness". Could someone briefly explain why this is true or give me some reference where i could find it?

Greetings, atajh