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

Abstract

In this paper, we refine the presentations of Behr and Mennicke [1] for SL(2,m)and PSL(2,m)wheremis odd. The group SL(2,m)is first shown to be presented by the following system of generators and relations:1.1The group PSL(2,m)appears as the factor group1.2This simplification then permits us to use the results of Schur [3] to establish three-relation presentations for these groups.