On Hurwitz generation and genus actions of sporadic groups
type: Item
instance of: scholarly article
title: On Hurwitz generation and genus actions of sporadic groups
zbMATH Open document ID: 0654.20014
author: Andrew J. Woldar
published in: Illinois Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 30F35
zbMATH DE Number: 4067182
zbMATH Keywords: (r,s,t)-generated
zbMATH Keywords: sporadic group
zbMATH Keywords: orientable surface
zbMATH Keywords: genus
zbMATH Keywords: orientation preserving
zbMATH Keywords: Hurwitz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4067182