Finite groups as a generalization of vector spaces through the use of splitting systems

Abstract

The structure of a finite group is investigated through a geometry induced by the splitting systems of the group. The method is based on the one used to induce a geometry on a finite dimensional vector space over a finite field and as a result, concepts related to the special and projective linear group are extended to arbitrary groups. One major by-product is the classification of solvable multiprimitive groups of arbitrary derived length. This leads to a necessary and sufficient condition for a solvable nC-group to be multiprimitive