Geodesic
Trees of diameter 4
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 2, pp. 475-494 
Yu. Yu. Kochetkov. Trees of diameter 4. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 2, pp. 475-494. http://geodesic.mathdoc.fr/item/FPM_2002_8_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We present a survey of works on Galois orbits of plane trees of diameter 4 with the central valency 4 and 5. Examples of nontrivial orbits are considered and criteria of a nontrivial decomposition are proved.

[1] Shabat G., Zvonkin A., “Plane trees and algebraic numbers”, Contemp. Math., 178 (1994), 233–275 | MR | Zbl

[2] Kochetkov Yu., “Ploskie derevya i ikh gruppy monodromii”, Uspekhi mat. nauk, 50:6 (1995), 163–164 | MR | Zbl

[3] Schneps L., “Dessins d'enfants on the Riemann sphere”, London Math. Soc. Lecture Notes, 200, Cambridge University Press., Cambridge, 1994, 47–77 | MR | Zbl

[4] Kochetkov Yu., “O netrivialno razlozhimykh tipakh”, Uspekhi mat. nauk, 52:4 (1997), 203–204 | MR | Zbl

[5] Leng S., Algebra, Mir, M., 1968