On Hurwitz generation and genus actions of sporadic groups
Let S be an orientable surface of least genus on which the finite group G acts in an orientation preserving manner. For G sporadic, \(G\neq McL\), \(Fi'_{24}\), we prove Aut(S) is isomorphic to G. Enroute to this result, we prove: (1) the only sporadics which fail to be (2,3,t)-generated are \(M_{11}\), \(M_{22}\), \(M_{23}\) and McL, and (2) of the 19 sporadics whose maximal subgroup structure is known, precisely seven are Hurwitz: \(J_ 1\), \(J_ 2\), He, Ru, \(Co_ 3\), HN and Ly.
scientific article; zbMATH DE number 4067182
scientific article