By Weil A.
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Extra resources for Collected papers. Vol.3 (1964-1978)
Now conjugacy of cartographic groups implies conjugacy of monodromy groups, but the converse is false: we shall give examples of dessins 28 Gareth Jones and Manfred Streit which have conjugate monodromy groups but non-conjugate cartographic groups. This shows that C is more effective than G in distinguishing orbits of G, but there is a price to be payed for this: doubling the degree of a permutation group can have a disproportionate effect on its size, so it can be much harder to compute C than G for a given dessin.
One can confirm algebraically that there are no other plane trees of this type. The elements go € Sr with cycle-structure a = 4,2,1 are all even, and form a single conjugacy class in Ar (consisting of its elements of order 4); similarly, the elements
Zvonkin, Plane trees and algebraic numbers, in Jerusalem Combinatorics 93 (H. Barcelo, G. ), Contemporary Mathematics, vol. 178, 1994, 233-275. Wielandt, Finite permutation groups. Academic Press, New YorkLondon, 1964. * Moscow State University adrianov@nw. mat h. msu. org Galois Groups, Monodromy Groups and Cartographic Groups Gareth A. Jones and Manfred Streit Abstract. The Riemann surfaces defined over the algebraic numbers are those admitting Belyi functions; such functions can be represented combinatorially by maps called dessins d'enfants, and these are permuted faithfully by the Galois group of the algebraic numbers.
Collected papers. Vol.3 (1964-1978) by Weil A.