Gassmann Equivalent Dessins

Abstract

This article studies pairs of dessins d'enfants that arise from Gassmann triples of groups (G, H, H′) together with pairs (g ₀, g ₁) of elements in G. We show that the two dessins have isomorphic monodromy groups, have the same branching data and the same number of components. Moreover, the sums of the genera of the components of the two dessins are the same. We give an example where the individual genera of the components of the first dessin differ from the genera of the components of the second dessin.

Key Words:

• Dessin d'enfant
• Gassmann triple

2000 Mathematics Subject Classification:

• 11G32
• 20B05

ACKNOWLEDGMENT

The first author would like to thank John Cullinan for the extremely helpful revision of this article.

Notes

Communicated by A. Turull.