Residual Properties of Free Groups Original Research Article

In this paper the following is proved: If X is an infinite class of finite simple groups of Lie-type such that the corresponding set of Lie-ranks is unbounded, then free groups of rank at least 2 are residually X. This is proved by the construction of special 2-generators for the classical finite simple groups if the Lie-rank is large enough ( ≥ 5 · 2130).