B7: Computations with matrix groups

The matrix group recognition project is an international research effort to design and implement efficient algorithms to work with groups of matrices defined over finite, and more recently also infinite, fields. Project B7 targets a difficult and important class of matrix groups over finite fields, namely the classical groups, which occur frequently as the building blocks of more general matrix groups and are vast already in small dimensions. Our aim is to design a novel second generation algorithm that takes as input a group, given by a set of matrices, which is already known to be isomorphic to a classical group and returns as output a data structure for the group. This data structure is essential for subsequent algorithms to answer questions about the group. Our algorithm is randomised and has to be accompanied by theorems which determine the probability of success and a rigorous complexity analysis of all steps. It will be implemented in OSCAR and tested on groups whose order is larger than 10^20.