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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)