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On Hurwitz generation and genus actions of sporadic groups. (English) Zbl 0654.20014
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.
Reviewer: A.J.Woldar

MSC:
20D08 Simple groups: sporadic groups
20F65 Geometric group theory
20F05 Generators, relations, and presentations of groups
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
20F29 Representations of groups as automorphism groups of algebraic systems
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
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