]. S. Bibliographie1, M. Abramov, &. M. Bronstein, and . Petkovsek, On Polynomial Solutions of Linear Operator Equations, Proceedings of ISSAC'95, pp.290-296, 1995.

E. Beke, Die Irreducibilit???t der homogenen linearen Differentialgleichungen, Mathematische Annalen, vol.45, issue.2, pp.278-294, 1894.
DOI : 10.1007/BF01446541

D. Bertrand, Groupes algébriques linéaires et théorie de Galois différentielle. Cours detroisì eme cycle, pp.1985-86, 1986.

F. Beukers, The maximal differential ideal is generated by its invariants, Indagationes Mathematicae, vol.11, issue.1, pp.13-18, 2000.
DOI : 10.1016/S0019-3577(00)88568-7

F. Beukers and &. G. Heckman, Monodromy for the hypergeometric function n F n ?1, Inventiones Mathematicae, vol.2, issue.2, pp.325-354, 1989.
DOI : 10.1007/BF01393900

H. F. Blichfeldt, On imprimitive linear homogeneous groups, Transactions of the American Mathematical Society, vol.6, issue.2, pp.230-236, 1905.
DOI : 10.1090/S0002-9947-1905-1500709-8

H. F. Blichfeldt, Finite collineation groups, 1917.
DOI : 10.1090/s0002-9904-1918-03116-9
URL : http://projecteuclid.org/download/pdf_1/euclid.bams/1183424613

D. Boucher, P. Gaillard, and &. F. Ulmer, Fourth order linear differential equations with imprimitive group, Proceedings of the 2003 international symposium on Symbolic and algebraic computation , ISSAC '03, 2003.
DOI : 10.1145/860854.860871

N. Bourbaki, Groupes et Algèbres de Lie, 1990.

M. Bronstein, On solutions of linear ordinary differential equations in their coefficient field, Journal of Symbolic Computation, vol.13, issue.4, pp.413-440, 1992.
DOI : 10.1016/S0747-7171(08)80106-X

M. Bronstein, An improved algorithm for factoring linear ordinary differential operators, Proceedings of the international symposium on Symbolic and algebraic computation , ISSAC '94, pp.336-340, 1994.
DOI : 10.1145/190347.190436

M. Bronstein, Computer Algebra Algorithms for Linear Ordinary Differential and Difference equations, Proceedings of the third European Congress of Mathematics, pp.105-119, 2001.
DOI : 10.1007/978-3-0348-8266-8_9

E. Compoint, Differential Equations and Algebraic Relations, Journal of Symbolic Computation, vol.25, issue.6, pp.705-725, 1998.
DOI : 10.1006/jsco.1997.0195

E. Compoint and &. M. Singer, Computing Galois Groups of Completely Reducible Differential Equations, Journal of Symbolic Computation, vol.28, issue.4-5, pp.473-494, 1999.
DOI : 10.1006/jsco.1999.0311

J. H. Conway, A. Hulpke, and &. J. Mckay, Abstract, LMS Journal of Computation and Mathematics, vol.1, pp.1-8, 1998.
DOI : 10.2307/2369906

O. Cormier, On Liouvillian solutions of linear differential equations of order 4 and 5, Proceedings of the 2001 international symposium on Symbolic and algebraic computation , ISSAC '01, 2001.
DOI : 10.1145/384101.384115

O. Cormier, Résolution deséquationsdeséquations différentielles linéaires d'ordre 4 et 5 : applicationsàapplicationsà la théorie de Galois classique, Thèse de doctorat, 2001.

D. Cox, J. Little, and &. Shea, Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra, 1997.

J. D. Dixon, The structure of linear groups, Van Nostrand Reinhold Mathematical Studies, 1971.

J. Draisma, Courriel sur le forum GAP, 2001.

J. Draisma, Courriel sur le forum GAP. 24 Août, 2001.

D. L. Flannery, The finite irreducible linear 2-groups of degree 4. Memoirs of the, Am. Math. Soc, vol.613, 1997.

D. L. Flannery, The Finite Irreducible Monomial Linear Groups of Degree 4, Journal of Algebra, vol.218, issue.2, pp.436-469, 1999.
DOI : 10.1006/jabr.1999.7883

D. L. Flannery, Irreducible monomial linear groups of degree four over finite fields. A para??trepara??tre dans, International Journal of Algebra and Computation

W. Fulton and &. J. Harris, Representation theory. A first course, GTM, vol.129, 1991.

P. Gaillard, Aspects du groupe de monodromie de l'´ equation hypergéométrique, 2000.

J. Hartmann, Invariants and Differential Galois Groups in Degree 4, Differential Galois Theory, 2002.

S. Hessinger, Computing the Galois Group of a Linear Differential Equation of Order Four, Applicable Algebra in Engineering, Communication and Computing, vol.11, issue.6, 1997.
DOI : 10.1007/s002000000055

S. Hessinger, Computing the Galois Group of a Linear Differential Equation of Order Four, Applicable Algebra in Engineering, Communication and Computing, vol.11, issue.6, pp.489-536, 2001.
DOI : 10.1007/s002000000055

M. Van-hoeij, Factorization of Differential Operators with Rational Functions Coefficients, Journal of Symbolic Computation, vol.24, issue.5, pp.537-561, 1997.
DOI : 10.1006/jsco.1997.0151

M. Van-hoeij, J. F. Ragot, F. Ulmer, and &. Weil, Liouvillian Solutions of Linear Differential Equations of Order Three and Higher, Journal of Symbolic Computation, vol.28, issue.4-5, pp.589-609, 1999.
DOI : 10.1006/jsco.1999.0316

M. Van-hoeij and &. Weil, An algorithm for computing invariants of differential Galois groups, Journal of Pure and Applied Algebra, vol.117, issue.118, pp.353-379, 1997.
DOI : 10.1016/S0022-4049(97)00018-2

B. Huppert, Endliche Gruppen I, 1967.
DOI : 10.1007/978-3-642-64981-3

E. L. Ince, Ordinary Differential Equations, The Mathematical Gazette, vol.18, issue.231, 1956.
DOI : 10.2307/3605524

I. and M. Isaacs, Character theory of finite groups, 1976.
DOI : 10.1090/chel/359

I. Kaplansky, An Introduction to Differential Algebra, 1957.

E. R. Kolchin, Algebraic Matric Groups and the Picard-Vessiot Theory of Homogeneous Linear Ordinary Differential Equations, The Annals of Mathematics, vol.49, issue.1, pp.1-42, 1948.
DOI : 10.2307/1969111

J. J. Kovacic, An algorithm for solving second order linear homogeneous differential equations, Journal of Symbolic Computation, vol.2, issue.1, pp.3-43, 1986.
DOI : 10.1016/S0747-7171(86)80010-4

G. Malle and &. H. Matzat, Inverse Galois Theory, 1999.
DOI : 10.1007/978-3-662-12123-8

J. Martinet and &. Ramis, Théorie de Galois différentielle et resommation, Computer Algebra and Differential Equations, pp.115-224, 1989.

C. Mitschi and &. M. Singer, Connected Linear Groups as Differential Galois Groups, Journal of Algebra, vol.184, issue.1, pp.333-361, 1996.
DOI : 10.1006/jabr.1996.0263
URL : https://hal.archives-ouvertes.fr/hal-00129541

C. Mitschi and &. M. Singer, Solvable-by-finite groups as differential Galois groups, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.11, issue.3, pp.403-423, 2002.
DOI : 10.5802/afst.1029
URL : https://hal.archives-ouvertes.fr/hal-00129674

J. Neubüser, H. Pahlings, and &. W. , Plesken. CAS ; Design and Use of a System for the Handling of Characters of Finite Groups. Dans Computational Group Theory, Proceedings of the London Mathematical Society Symposium on Computational Group Theory. M.D. AtkinsonédAtkinsonéd, 1984.

A. Person, Solving homogenous linear differential equations of order 4 in terms of equations of smaller order, Thèse de doctorat, 2002.

M. Van-der-put and &. M. Singer, Differential Galois Theory. Grundlehren der mathematischen Wissenschaften 328, 2003.

M. Van-der-put and &. F. Ulmer, Differential Equations and Finite Groups, Journal of Algebra, vol.226, issue.2, pp.920-966, 2000.
DOI : 10.1006/jabr.1999.8209

D. J. Robinson, A Course in the Theory of Groups, GTM, vol.80, 1982.

L. Schmidt-thieme, Lineare Differentialoperatoren mit endlicher Galoisgruppe, Diplomarbeit. IWR, 1999.

M. F. Singer, Algebraic solutions of n-th order linear differential equations, Proceedings on the 1979 Queens Conference on Number Theory, pp.379-420, 1980.

M. F. Singer, Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations, American Journal of Mathematics, vol.103, issue.4, pp.661-682, 1981.
DOI : 10.2307/2374045

M. F. Singer, Solving Homogeneous Linear Differential Equations in Terms of Second Order Linear Differential Equations, American Journal of Mathematics, vol.107, issue.3, pp.663-696, 1985.
DOI : 10.2307/2374373

M. F. Singer, Algebraic Relations Among Solutions of Linear Differential Equations: Fano's Theorem, American Journal of Mathematics, vol.110, issue.1, pp.115-144, 1988.
DOI : 10.2307/2374541

M. F. Singer, Testing reducibility of linear differential operators: A group theoretic perspective, Applicable Algebra in Engineering, Communication and Computing, vol.16, issue.No. 2, pp.77-104, 1996.
DOI : 10.1007/BF01191378

M. F. Singer and &. F. Ulmer, Galois Groups of Second and Third Order Linear Differential Equations, Journal of Symbolic Computation, vol.16, issue.1, pp.1-36, 1993.
DOI : 10.1006/jsco.1993.1032

M. F. Singer and &. F. Ulmer, Liouvillian and Algebraic Solutions of Second and Third Order Linear Differential Equations, Journal of Symbolic Computation, vol.16, issue.1, pp.37-73, 1993.
DOI : 10.1006/jsco.1993.1033

M. F. Singer and &. F. Ulmer, Necessary conditions for liouvillian solutions of (third order) linear differential equations, Applicable Algebra in Engineering, Communication and Computing, vol.2, issue.1, pp.1-22, 1995.
DOI : 10.1007/BF01270928

M. F. Singer and &. F. Ulmer, Linear differential equations and products of linear forms, Journal of Pure and Applied Algebra, vol.117, issue.118, pp.549-563, 1997.
DOI : 10.1016/S0022-4049(97)00027-3

L. Smith, Polynomial Invariants of Finite Groups. A K Peters, 1995.

T. A. Springer, Linear algebraic groups, 1998.

B. Sturmfels, Algorithms in invariant theory, 1993.
DOI : 10.1007/978-3-7091-4368-1

F. Ulmer, On liouvillian solutions of linear differential equations, Applicable Algebra in Engineering, Communication and Computing, vol.2, issue.3, pp.171-193, 1992.
DOI : 10.1007/BF01294332

F. Ulmer, Introduction to differential Galois theory, 2000.

F. Ulmer, Liouvillian solutions of third order differential equations, Journal of Symbolic Computation, vol.36, issue.6, pp.855-889, 2003.
DOI : 10.1016/S0747-7171(03)00065-8

F. Ulmer, Note on algebraic solutions of differential equations with known finite Galois group, Applicable Algebra in Engineering, Communication and Computing, vol.28, issue.4, 2003.
DOI : 10.1007/s00200-005-0177-9