Computing automorphisms of finite soluble groups

Abstract

There is a large collection of effective algorithms for computing information about finite soluble groups. The success in computation with these groups is primarily due to a computationally convenient representation of them by means of (special forms of) power conjugate presentations. A notable omission from this collection of algorithms is an effective algorithm for computing the automorphism group of a finite soluble group. An algorithm designed for finite groups in general provides only a partial answer to this deficiency. In this thesis an effective algorithm for computing the automorphism group of a finite soluble group is described. An implementation of this algorithm has proved to be a substantial improvement over existing techniques available for finite soluble groups.