Finite linear groups as differential Galois groups. (Q2777731)

The inverse problem in differential Galois theory is considered. An effective construction of linear differential equations with a given finite linear group as the Galois group is developed. The method presented is a refinement of the method proposed by Singer and Ulmer. Special attention is paid to the case of differential equations with the Galois groups \(A_4\), \(S_4\), and \(A_5\). Explicit examples of irreducible differential equations of order 4 and 3 over \(\overline{\mathbb Q}(T)\) with Galois group \(A_5\) are presented.