Do morphisms of algebraic groups have any special properties ? I am mainly interested in morphisms between algebraic groups preserving the group structure; but I am also interested
in arbitrary morphisms between algebraic groups. For example, 

> what can be said about the morphism $x^n: G \rightarrow G$, $x$ goes into $x^n$: 
>is it necessary proper? finite? when is it etale? what if $G$ is commutative but not necessarily an abelian variety?




In fact, I am rather looking for a <i>reference</i> which describes 
such properties in full generality: that is, between arbitrary 
(finite dimensional), possibly commutative, algebraic groups 
in arbitrary characteristic.