Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Valentiner group as Galois group


Authors: Teresa Crespo and Zbigniew Hajto
Journal: Proc. Amer. Math. Soc. 133 (2005), 51-56
MSC (2000): Primary 12F12; Secondary 11F80, 12H05
Published electronically: August 20, 2004
MathSciNet review: 2085152
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We obtain the complete set of solutions to the Galois embedding problem given by the Valentiner group as a triple cover of the alternating group $A_6$.


References [Enhancements On Off] (What's this?)

  • 1. Teresa Crespo and Zbigniew Hajto, Finite linear groups as differential Galois groups, Bull. Polish Acad. Sci. Math. 49 (2001), no. 4, 361–373. MR 1872670
  • 2. Teresa Crespo and Zbigniew Hajto, Recouvrements doubles comme groupes de Galois différentiels, C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), no. 4, 271–274 (French, with English and French summaries). MR 1854763, 10.1016/S0764-4442(01)02075-4
  • 3. T. Crespo and Z. Hajto, Differential Galois realization of double covers, Ann. Inst. Fourier (Grenoble) 52 (2002), no. 4, 1017–1025 (English, with English and French summaries). MR 1926670
  • 4. I. Martin Isaacs, Character theory of finite groups, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure and Applied Mathematics, No. 69. MR 0460423
  • 5. J.-F. Mestre, Extensions 𝑄-régulières de 𝑄(𝑡) de groupe de Galois 6.𝐴₆ et 6.𝐴₇, Israel J. Math. 107 (1998), 333–341 (French, with English summary). MR 1658587, 10.1007/BF02764017
  • 6. G.A. Miller, H.F. Blichfeldt, L.E. Dickson, Theory and applications of finite groups, John Wiley and Sons, Inc., 1916.
  • 7. Michael F. Singer, An outline of differential Galois theory, Computer algebra and differential equations, Comput. Math. Appl., Academic Press, London, 1990, pp. 3–57. MR 1038057
  • 8. Marius van der Put and Michael F. Singer, Galois theory of linear differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 328, Springer-Verlag, Berlin, 2003. MR 1960772

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 12F12, 11F80, 12H05

Retrieve articles in all journals with MSC (2000): 12F12, 11F80, 12H05


Additional Information

Teresa Crespo
Affiliation: Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
Email: crespo@mat.ub.es

Zbigniew Hajto
Affiliation: Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
Address at time of publication: Zakład Matematyki, Akademia Rolnicza, al. Mickiewicza 24/28, 30-059 Kraków, Poland
Email: rmhajto@cyf-kr.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07539-2
Received by editor(s): June 3, 2003
Received by editor(s) in revised form: October 9, 2003
Published electronically: August 20, 2004
Additional Notes: The first author was supported in part by BFM2000-0794-C02-01, Spanish Ministry of Education
Communicated by: Lance W. Small
Article copyright: © Copyright 2004 American Mathematical Society