Paper Info
Title
Explicit Galois realization of transitive groups of degree up to 15
Abstract
We describe methods for the construction of polynomials with certain types of Galois groups. As an application we deduce that all transitive groups G up to degree 15 occur as Galois groups of regular extensions of Q ( t ), and in each case compute a polynomial f ∈ Q [ x ] with Gal ( f ) = G . References References 1 V. Acciaro J. Klüners Computing automorphisms of abelian number fields Math. Comput. 68 1999 1179 1186 2 J. Buchmann H. Lenstra Approximating rings of integers in number fields J. Theor. Nombres Bordx. 2 1994 221 260 3 H. Cohen A Course in Computational Algebraic Number Theory 1993 Springer Berlin 4 J.H. Conway A. Hulpke J. McKay On transitive permutation groups J. Comput. Math. 1 1998 1 8 5 M. Daberkow C. Fieker J. Klüners M. Pohst K. Roegner K. Wildanger KANT V4 J. Symb. Comput. 24 1997 267 283 6 Y. Eichenlaub, 1996 7 C. Fieker, 1997 8 K. Geissler J. Klüners Galois group computation for rational polynomials J. Symb. Comput 30 2000 653 674. doi:10.1006/jsco.2000.0377 9 K. Girstmair On the computation of resolvents and Galois groups Manuscr. Math. 43 1983 289 307 10 G. Kemper A. Steel Some algorithms in invariant theory of finite groups P. Dräxler G. Michler C.M. Ringel Proceedings of the Euroconference on Computational Methods for Representations of Groups and Algebras, Progress in Mathematics 1999 Birkhäuser Basel 11 J. Klüners, 1997 12 J. Klüners On computing subfields—a detailed description of the algorithm J. Théorie Nombres Bord. 10 1998 243 271 13 J. Klüners, G. Malle 14 J. Klüners M. Pohst On computing subfields J. Symb. Comput. 24 1997 385 397 15 A. Ledet Subgroups of Hol Q 8 as Galois groups J. Algebra 181 1996 478 506 16 A.K. Lenstra H.W. Lenstra Jr. L. Lovász Factoring polynomials with rational coefficients Math. Ann. 261 1982 515 534 17 G. Malle Polynomials for primitive nonsolvable permutation groups of degree d ≤ 15 J. Symb. Comput. 4 1987 83 92 18 G. Malle B.H. Matzat Realisierung von Gruppen PSL 2 ( F p ) als Galoisgruppen über Q Math. Ann. 272 1985 549 565 19 G. Malle B.H. Matzat Inverse Galois Theory 1999 Springer Verlag Heidelberg 20 M.E Pohst H. Zassenhaus Algorithmic Algebraic Number Theory, Encyclopaedia of Mathematics and its Applications 1989 Cambridge University Press 21 M. et al. , Schönert 22 M. Suzuki Group Theory 1982 Springer New York
Year
DOI
Venue
2000
10.1006/jsco.2000.0378
J. Symb. Comput.
Keywords
DocType
Volume
Explicit Galois realization,transitive group
Journal
30
Issue
ISSN
Citations 
6
Journal of Symbolic Computation
7
PageRank 
References 
Authors
1.17
3
2
Name
Order
Citations
PageRank
JüRgen KlüNers14910.32
Gunter Malle2289.42