Factorisations explicites de g(y) - h(z)

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1. [1] N. M. Adrianov, Classification des groupes cartographiques primitifs des arbres plans, Fundamental'naya i prikladnaya matematika 3, 1997 (en Russe). 
2. [2] N. M. Adrianov, Yu. Kotchetkov et A. D. Souvorov, Arbres planaires avec des groupes cartographiques exceptionnels, preprint, 1997 (en Russe). 
3. [3] C. Batut, K. Belabas, D. Bernardi, H. Cohen and M. Olivier, User's guide to PARI-GP, Université de Bordeaux, 1996. 
4. [4] G. D. Birkhoff and H. S. Vandiver, On the integral divisors of $a^n-b^n$, Ann. of Math. 5 (1903), 173-180. Zbl35.0205.01
5. [5] W. Bosma et al., Magma Reference Manual, http://www.maths.usyd.edu.au, 1997. 
6. [6] W. Burnside, On simply transitive groups of prime degree, Quart. J. Math. 37 (1906), 215-221. Zbl37.0172.01
7. [7] R. D. Carmichael, Introduction to the Theory of Groups of Finite Order, Ginn, Boston, 1937. Zbl0019.19702
8. [8] J. W. S. Cassels, Factorization of polynomials in several variables, in: Proc. 15th Scandinavian Congress, Oslo, Lecture Notes in Math. 118, Springer, 1968, 1-17. 
9. [9] B. W. Char et al., Maple V Language Reference Manual, Springer, 1991. Zbl0758.68038
10. [10] C. Chevalley, Thèses, Faculté des sciences de l'Université de Paris, 1934. 
11. [11] J. Conway et al., Atlas of Finite Groups, Clarendon Press, 1985. 
12. [12] C. W. Curtis, W. M. Kantor and G. M. Seitz, The 2-transitives permutations representations of the finite Chevalley groups, Trans. Amer. Math. Soc. 218 (1976), 1-59. Zbl0374.20002
13. [13] H. Davenport, D. J. Lewis and A. Schinzel, Equations of the form f(x)=g(y), Quart. J. Math. Oxford Ser. 12 (1961), 304-312. Zbl0121.28403
14. [14] H. Davenport and A. Schinzel, Two problems concerning polynomials, J. Reine Angew. Math. 214 (1964), 386-391. Zbl0152.02303
15. [15] P. Dembowski, Finite Geometries, Springer, 1968. Zbl0159.50001
16. [16] D. Dixon, The Structure of Linear Groups, Van Nostrand Reinhold, 1971. Zbl0232.20079
17. [17] L. Schneps (ed.), The Theory of Grothendieck's Dessins d'Enfant, Cambridge University Press, 1994. 
18. [18] W. Feit, Automorphisms of symmetric balanced incomplete block designs, Math. Z. 118 (1970), 40-49. Zbl0204.32702
19. [19] W. Feit, On symmetric balanced incomplete block designs with doubly transitive automorphism groups, J. Combin. Theory Ser. A 14 (1973), 221-247. Zbl0278.05016
20. [20] W. Feit, Some consequences of the classification of finite simple groups, in: Proc. Sympos. Pure Math. 37, Amer. Math. Soc., 1980, 175-181. Zbl0454.20014
21. [21] M. Fried, On a conjecture of Schur, Michigan Math. J. 17 (1970), 41-55. 
22. [22] M. Fried, The field of definition of function fields and a problem in the reducibility of polynomials in two variables, Illinois J. Math. 17 (1973), 128-146. Zbl0266.14013
23. [23] M. Fried, Exposition on an arithmetic-group theoretic connection via Riemann's existence theorem, in: Proc. Sympos. Pure Math. 37, Amer. Math. Soc., 1980, 571-602. 
24. [24] M. Hall, Jr., The Theory of Groups, Macmillan, 1959. 
25. [25] S. Lang, Algebra, Addison-Wesley, 1984. 
26. [26] P. Müller, Primitive monodromy groups for polynomials, in: Recent Developments in the Inverse Galois Problem, M. Fried (ed.), Contemp. Math. 186, Amer. Math. Soc., 1995, 385-401. Zbl0840.12001
27. [27] H. J. Ryser, Combinatorial Mathematics, Wiley, 1963. Zbl0112.24806
28. [28] I. Schur, Zur Theorie der einfach transitiven Permutationsgruppen, Preuss. Akad. Wiss. Phys.-Math. Kl. 1933, 598-623. Zbl59.0151.01
29. [29] J. Singer, A theorem in finite projective geometry and some applications to number theory, Trans. Amer. Math. Soc. 43 (1938), 377-385. Zbl64.0972.04
30. [30] J. A. Todd, A combinatorial problem, J. Math. Phys. Mass. Inst. Tech. 12 (1933), 321-333. Zbl0007.10005

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