  Let $G$ be a connected, absolutely almost simple, algebraic group defined
over a finitely generated, infinite field $K$, and let $\Gamma$ be a Zariski
dense subgroup of $G(K)$. We show, apart from some few exceptions, that the
commensurability class of the field $\mathcal{F}$ given by the compositum of
the splitting fields of characteristic polynomials of generic elements of
$\Gamma$ determines the group $G$ upto isogeny over the algebraic closure of
$K$.
