Algorithms for the Tits alternative and related problems

We present an algorithm to decide whether a finitely generated linear group over an infinite field is solvable-by-finite, thereby obtaining a computationally effective version of the Tits alternative. We also give algorithms to decide whether the group is nilpotent-by-finite, abelian-by-finite, or central-by-finite. Implementations of the algorithms are publicly available in Magma.