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We show that the least genus of any compact Riemann surface S, admitting a simple Suzuki group G = Sz(^) as a group of automorphisms, is equal to 1 +|G|/40. We compute the number of such surfaces S as the number of normal subgroups of the triangle group A(2,4,5) with quotient-group G, and investigate the associated regular maps of type {4,5}.

- E Bujalance, A F Costa, D Singerman
- 1993

Let X be a compact Riemann surface of genus g > 1. A symmetry S of X is an anticonformal involution. We write jSj for the number of connected components of the xed points set of S. Suppose that X admits two distinct symmetries S 1 and S 2 ; then we nd a bound for jS 1 j + jS 2 j in terms of the genus of X and the order of S 1 S 2. We discuss circumstances… (More)

- Cori Hypermaps, Dessins d’Enfants, David Singerman, Jürgen Wolfart
- 2008

This paper explains some facts probably known to experts and implicitely contained in the literature about dessins d'enfants but which seem to be nowhere explicitely stated. The 1-skeleton of every regular Cori hypermap is the Cayley graph of its automorphism group, embedded in the underlying orientable surface. Conversely, every Cayley graph of a finite… (More)

- DAVID SINGERMAN
- 2006

- Ramsey Michael Faragher, Stanislav Shabala, George Vardulakis, Michael Bridges, Anna Scaife, Emily Curtis +14 others
- 2009

- David Singerman
- 2006

Introduction Belyi's Theorem [Be] of 1979 had a profound effect on Galois Theory, Riemann surfaces and complex algebraic curves. It led Grothendieck [Gr] to develop his theory of dessins d'enfants in which there has been a great interest. The theory is about embedding graphs into compact Riemann surfaces. For further applications to topics such as such as… (More)