Abstract

The ability to distinguish permutation isomorphism classes of groups is an important step in the computation of Galois groups of polynomials over the rationals. In order to distinguish permutation isomorphism classes of groups, it is useful to have an extensive list of their invariants. These invariants include properties such as the order, imprimitivity, parity and shapes, as well as the orbit lengths of sets and sequences. Computing these characteristics can be extremely time consuming. In this thesis, a detailed description of efficient algorithms for solving the problem using the concept of expanding horizon and orbit computation is presented.