Presentations of the Groups SL(2,m) And PSL(2,m)

In this paper, we refine the presentations of Behr and Mennicke [ 1 ] for SL(2, m) and PSL(2, m) where m is odd. The group SL(2, m) is first shown to be presented by the following system of generators and relations: 1.1 The group PSL(2, m) appears as the factor group 1.2 This simplification then permits us to use the results of Schur [3] to establish three-relation presentations for these groups.