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A family of Hurwitz groups with non-trivial centres

  • Marston Conder (a1)
Abstract

In this paper a new family of quotients of the triangle group < x, y, z | x2 = y3 = z7 = xyz = 1 > is obtained. It is shown that for every positive integer m divisible by 3 there is a Hurwitz group of order 504m6 having a centre of size 3, and as a consequence there is a Riemann surface of genus 6m6 + 1 with the maximum possible number of automorphisms.

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[1]J.J. Cannon , L.A. Dimino , G. Havas and J.M. Watson , “Implementation and analysis of the Todd-Coxeter algorithm”, Math. Comp. 27 (1973), 463490.

[4]A. Hurwitz , “Über algebraische Gebilde mit eindeutigen Transformationen in sich”, Math. Ann. 41 (1983), 403442.

[8]Chih – han Sah , “Groups related to compact Riemann surfaces”, Acta Mathematica 123 (1969), 1342.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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