---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/GlobalFields/GaloisGroupsAndAutomorphisms/bibliography.html"
source: "https://docs.magma-maths.org/GlobalFields/GaloisGroupsAndAutomorphisms/bibliography.md"
part: "Global Fields"
chapter: "Galois Groups and Automorphisms"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Global Fields", "source": "../index-global-fields.md"}
  - {"title": "Galois Groups and Automorphisms", "source": "index-galois-groups-and-automorphisms.md"}
prev: {"title": "Automorphisms of Fields", "source": "fld_auts.md"}
next: {"title": "Class Field Theory", "source": "../ClassFieldTheory/index-class-field-theory.md"}
---

# Bibliography

<a id="cite-ackl1"></a>
- **[AK99]** Vincenzo Acciaro and Jürgen Klüners. Computing Automorphisms of Abelian Number Fields. *Math. Comp.*, 68(227):1179–1186, 1999.
<a id="cite-poonen2004"></a>
- **[BDE+]** N. Berry, A. Dubickas, N. Elkies, B. Poonen, C. Smyth. “The conjugate dimension of algebraic numbers.” Quart. J. Math., 55, 237–252.
<a id="cite-degraaffieker"></a>
- **[dGF07]** Willem de Graaf and Claus Fieker. Finding integral linear dependencies of algebraic numbers and algebraic Lie algebras. *LMS Journal of Computation and Mathematics*, 11:, 2007.
<a id="cite-elsenhans-paper"></a>
- **[Els12]** A.-S. Elsenhans. Invariants for the computation of intransitive and transitive Galois groups. *Journal of Symbolic Computation*, 47:315–326, 2012.
<a id="cite-elsenhans-short"></a>
- **[Els14]** A.-S. Elsenhans. A Note on Short Cosets. *Experimental Mathematics*, 23:411–413, 2014. [doi:10.1080/10586458.2014.922908](https://doi.org/10.1080/10586458.2014.922908).
<a id="cite-elsenhans-improved-relative-invariants"></a>
- **[Els16]** Andreas-Stephan Elsenhans. Improved methods for the construction of relative invariants for permutation groups. To appear in Journal of Symbolic Computation, Available online since 5 February 2016, 2016. [doi:10.1016/j.jsc.2016.02.005](https://doi.org/10.1016/j.jsc.2016.02.005).
<a id="cite-fieker-galois"></a>
- **[FK14]** C. Fieker and J. Klüners. Computation of Galois Groups of Rational Polynomials. *London Mathematical Society Journal of Computation and Mathematics*, 17(1):141 – 158, 2014. http://arxiv.org/abs/1211.3588.
<a id="cite-geissler"></a>
- **[Gei03]** Katharina Geißler. *Berechnung von Galoisgruppen über Zahl- und Funktionenkörpern*. PhD Thesis, TU-Berlin, 2003. available at http://www.math.tu-berlin.de/ kant/publications/diss/geissler.pdf.
<a id="cite-gk1"></a>
- **[GK00]** Katharina Geißler and Jürgen Klüners. Galois Group computation for Rational Polynomials. *J. Symbolic Comp.*, 30(6):653–674, 2000.
<a id="cite-kl1"></a>
- **[Klu95]** Jürgen Klüners. Über die Berechnung von Teilkörpern algebraischer Zahlkörper. Master's thesis, Technische Universität Berlin, 1995. http://www.math.tu-berlin.de/$\sim$kant/publications/diplom/klueners.ps.gz.
<a id="cite-kl2"></a>
- **[Klu97]** Jürgen Klüners. *Über die Berechnung von Automorphismen und Teilkörpern algebraischer Zahlkörper*. Dissertation, Technische Universität Berlin, 1997. http://www.math.tu-berlin.de/$\sim$kant/publications/diss/diss_jk.ps.gz.
<a id="cite-kl3"></a>
- **[Klu98]** Jürgen Klüners. On computing subfields. A detailed description of the algorithm. *J. Theor. Nombres Bordx.*, 2(10):243–271, 1998.
<a id="cite-klpo1"></a>
- **[KP97]** Jürgen Klüners and Michael E. Pohst. On Computing Subfields. *J. Symbolic Comp.*, 24(3):385–397, 1997.
<a id="cite-mk2"></a>
- **[SM85]** Leonhard H. Soicher and John McKay. Computing Galois Groups over the rationals. *J. Number Th.*, 20:273–281, 1985.
<a id="cite-stau"></a>
- **[Sta73]** Richard P. Stauduhar. The determination of Galois Groups. *Math. Comp.*, 27:981–996, 1973.
<a id="cite-suth-galois"></a>
- **[Sut15]** Nicole Sutherland. Computing Galois Groups of Polynomials (especially over Function Fields of Prime Characteristic). *Journal of Symbolic Computation*, 71:73–97, 2015. [doi:10.1016/j.jsc.2014.09.043](https://doi.org/10.1016/j.jsc.2014.09.043).
<a id="cite-vanhoeijklueners"></a>
- **[vHKN11]** M. van Hoeij, J. Klüners, and A. Novocin. Generating Subfields. In Anton Leykin, editor, *Proceedings ISSAC 2011*. 2011.