Algorithms for linear groups of finite rank

A. S. Detinko, D. L. Flannery, E. A. O'Brien

Published 2019-05-11Version 1

Let $G$ be a finitely generated solvable-by-finite linear group. We present an algorithm to compute the torsion-free rank of $G$ and a bound on the Pr\"{u}fer rank of $G$. This yields in turn an algorithm to decide whether a finitely generated subgroup of $G$ has finite index. The algorithms are implemented in MAGMA for groups over algebraic number fields.