Linear representations of groups generated by reflections

The following theorem is proved: two groups $\Gamma_1$ and $\Gamma_2$ acting discretely on $\Lambda^3$, with compact factor-space and isomorphic, as abstract groups, to a group generated by reflections, are conjugate in the group of motions of $\Lambda^3:g\Gamma_1g^{-1}=\Gamma_2$.
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