Genus One Almost Simple Groups of Lie Rank Two


In this paper, we assume that G is a finite group with socle PSL(3,q) and G acts on the projective points of 2-dimensional projective geometry PG(2,q), q is a prime power. By using a new method, we show that G possesses no genus one group if q>13. Furthermore, we study the connectedness of the Hurwitz space \mathcal{H}^{in}_{r}(G) for a given group G, genus one and q\leq 13.

DOI Code: 10.1285/i15900932v43n2p67

Keywords: Projective special linear group; Fixed point ratio; Genus one group

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