A Presentation of the Groups PSL(2, p) with Three Defining Relations
Hans J. Zassenhaus · Canadian Journal of Mathematics · 1969
H. Behr and J. Mennicke (1) have proven that the group PSL(2, p) can be presented by the following system of generators and relations: 1 From this presentation, it follows that the three relations 2 for the same generators S and T suffice if p > 3, p ≠ 17. If p = 3, it is well known that the relations S3 = 1, T2 = 1, and (ST)3 = 1 define PSL(2, 3). For p = 2, the relations S3 = 1, T2 = 1, and (ST)2 = 1 define PSL(2, 2). For p = 17, the three relations 3 will suffice. Indeed, the group G, with generators S, T and defining relations (2), contains the subgroup 〈Sp〉 in its centre.