The application of computeralgebra within the fundamental research in geometry and theory of groups.

This project reflects a new view on mathematics and the use of computers. The genesis of new software for symbolic computation enables an experimental approach to mathematics. The aim of this project is to use computer algebra software for research on finite geometry and group theory. We shall, as is usual in natural sciences, do experiments to get better understanding of abstract problems. This will lead to conjectures which will develop into a new theory. Comparing different (theoretical) methods will also be part of our project.Specific programming languages will be used for computing with groups and geometry. These demand a lot of CPU time and memory.This research is part of the quest for a generalization of an existing theory which provides a geometric interpretation of abstract groups. In particular it will enable us to study an infinite family of groups which cannot be included in the existing theory.