A note on free products of linear groups

Abstract:

For a field $K$, let $\bar K$ denote its algebraic closure. Assume that $\left | {\bar K:K} \right | = \infty$. Then for any linear groups $G,{\text { }}H \subseteq {\text {G}}{{\text {L}}_n}(K)$ their free product $G * H$ can be embedded into ${\text {G}}{{\text {L}}_N}(K(t))$. Here $N$ is an integer depending on $K$ only and $t$ stands for an indeterminate.