Geodesic
A Presentation of the Groups PSL(2, p) with Three Defining Relations
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 310-311

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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 S 3 = 1, T 2 = 1, and (ST)3 = 1 define PSL(2, 3). For p = 2, the relations S 3 = 1, T 2 = 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. 
Zassenhaus, Hans J. A Presentation of the Groups PSL(2, p) with Three Defining Relations. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 310-311. doi: 10.4153/CJM-1969-032-8
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[1] 1. Behr, H. and Mennicke, J., A presentation of the groups PSL(2, p), Can. J. Math. 20 (1968), 1432–1438. Google Scholar

[2] 2. Schur, I., Untersuchungen iiber die Darstellungen der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 182 (1907), 85–137. Google Scholar

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