Computational Aspects of Group Extensions and Their Applications in Topology
Karel Dekimpe, Bettina Eick · Experimental Mathematics · 2002
We describe algorithms to determine extensions of infinite polycyclic groups having certain properties. In particular, we are interested in torsion-free extensions and extensions whose Fitting subgroup has a minimal centre. Then we apply these methods in topological applications. We discuss the calculation of Betti numbers for compact manifolds, and we describe algorithmic approaches in classifying almost Bieberbach groups.