Polynomials for primitive nonsolvable permutation groups of degree d\(\leq 15\)
All nonsolvable groups having a faithful primitive permutation representation of degree \(\leq 15\) are known to occur as Galois groups over \({\mathbb{Q}}\). A constructive method of computing polynomials having one of these groups as Galois groups has been given by \textit{B. H. Matzat} [J. Reine Angew. Math. 349, 179-220 (1984; Zbl 0555.12005)]. Previous results obtained by Matzat (loc. cit.), the author and \textit{B. H. Matzat} [Math. Ann. 272, 549-565 (1985; Zbl 0559.12005)], and \textit{B. H. Matzat} and \textit{A. Zeh-Marschke} [J. Number Theory 23, 195-202 (1986; Zbl 0598.12007)] show that only polynomials with Galois groups \(PGL(2,11)\), \(PSL(3,3)\), \(Hol(E_ 8)\) (the holomorph of an elementary abelian group of order 8) remain to be determined. The author fills in the gap by computing the required polynomials.
scientific article; zbMATH DE number 4027612