Dessins d'Enfants on Riemann Surfaces by Gareth A. Jones & Jürgen Wolfart

Author:Gareth A. Jones & Jürgen Wolfart
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Exercise 5.11

Use Table 5.6 in Sect. 5.5 to deal with the case in Example 5.11 where , that is, . (Warning: if , that is, , then the irreducible characters of degree p − 1 and all contribute to the sum in Proposition 5.2.)

This technique has been applied to other finite groups, for instance in [28] to count the Hurwitz surfaces associated with the Ree groups R(3 e ), and in [30] to count the quotients of Δ(2, 4, 5) isomorphic to the Suzuki groups Sz(2 e ); see Sect. 2.​2.​3 for these families of finite simple groups.

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