Finite fields in elliptic curve I have an elliptic curve defined over finite field where $S_1=aP$ . Is it valid to say that $S_1P$ can also be computed.  $P$ is the generator of the group.
What my real question is that. Should '$a$' be always an integer or can it be a group element itself??
Should '$a$' be always an integer or can it be a group element itself??


Well, $aP$ is defined to be:

$aP \equiv \underbrace{P + P + \ldots + P}_\text{a times}$

From that definition, we see that this makes sense only if $a$ is an integer; it needs to be a count of the number of $P$'s to add together.