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

On the splitting fields of generic elements in Zariski dense subgroups