This paper continues previous work, based on systematic use of a formula of L. Scott, to detect Hurwitz groups. It closes the problem of determining the finite simple groups contained in PGL_n(F) for n ≤ 7 which are Hurwitz, where F is an algebraically closed field. For the groups G2(q), q ≥ 5, and the Janko groups J_1 and J_2 it provides explicit (2, 3, 7)-generators.
Pellegrini, M. A., Tamburini Bellani, M. C., Scott's formula and Hurwitz groups, <<JOURNAL OF ALGEBRA>>, 2015; 443 (N/A): 126-141. [doi:10.1016/j.jalgebra.2015.07.011] [http://hdl.handle.net/10807/68317]
Scott's formula and Hurwitz groups
Pellegrini, Marco Antonio;Tamburini Bellani, Maria Clara
2015
Abstract
This paper continues previous work, based on systematic use of a formula of L. Scott, to detect Hurwitz groups. It closes the problem of determining the finite simple groups contained in PGL_n(F) for n ≤ 7 which are Hurwitz, where F is an algebraically closed field. For the groups G2(q), q ≥ 5, and the Janko groups J_1 and J_2 it provides explicit (2, 3, 7)-generators.
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