---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/FiniteGroups/DatabasesOfGroups/bibliography.html"
source: "https://docs.magma-maths.org/FiniteGroups/DatabasesOfGroups/bibliography.md"
part: "Finite Groups"
chapter: "Databases of Groups"
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  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Finite Groups", "source": "../index-finite-groups.md"}
  - {"title": "Databases of Groups", "source": "index-databases-of-groups.md"}
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---

# Bibliography

<a id="cite-besche-eick-constr"></a>
- **[BE99a]** Hans Ulrich Besche and Bettina Eick. Construction of finite groups. *J. Symbolic Comput.*, 27(4):387–404, 1999.
<a id="cite-besche-eick-1000"></a>
- **[BE99b]** Hans Ulrich Besche and Bettina Eick. The groups of order at most 1000 except 512 and 768. *J. Symbolic Comput.*, 27(4):405–413, 1999.
<a id="cite-besche-eick-order-qnp"></a>
- **[BE01]** Hans Ulrich Besche and Bettina Eick. The groups of order $q\sp n\cdot p$. *Comm. Algebra*, 29(4):1759–1772, 2001.
<a id="cite-besche-eick-obrien-order-2000"></a>
- **[BEO01]** Hans Ulrich Besche, Bettina Eick, and E. A. O'Brien. The groups of order at most 2000. *Electron. Res. Announc. Amer. Math. Soc.*, 7:1–4 (electronic), 2001.
<a id="cite-bratus-pak"></a>
- **[BP00]** Sergey Bratus and Igor Pak. Fast constructive recognition of a black box group isomorphic to $S_n$ or $A_n$ using Goldbach's conjecture. *J. Symbolic Comp.*, 29:33–57, 2000.
<a id="cite-trans32"></a>
- **[CH08]** J.J. Cannon and D.F. Holt. The transitive permutation groups of degree 32. *Experiment. Math.*, 17:307–314, 2008.
<a id="cite-prim4096"></a>
- **[CQRD11]** Hannah J. Coutts, Martyn Quick, and Colva M. Roney-Dougal. The primitive permutation groups of degree less than 4096. *Communications in Algebra*, 39:10:3526–3546, 2011.
<a id="cite-dietrich-eick"></a>
- **[DE05]** Heiko Dietrich and Bettina Eick. On the groups of cubefree order. *J. Algebra*, 292:122–137, 2005.
<a id="cite-dep4primes"></a>
- **[DEP22]** Heiko Dietrich, Bettina Eick, and Xueyu Pan. Groups whose orders factorise into at most four primes. *J. Symbolic Comput.*, 108:23–40, 2022. URL: [https://doi.org/10.1016/j.jsc.2021.04.005](https://doi.org/10.1016/j.jsc.2021.04.005), [doi:10.1016/j.jsc.2021.04.005](https://doi.org/10.1016/j.jsc.2021.04.005).
<a id="cite-virtualhaken"></a>
- **[DT03]** Nathan M. Dunfield and William P. Thurston. The virtual Haken conjecture; experiments and examples. *Geometry & Topology*, 7:399–441, 2003.
<a id="cite-holtroyle"></a>
- **[HR19]** D. Holt and G. Royle. A census of small transitive groups and vertex-transitive graphs. *J. Symb. Comput.*, 2019. https://doi.org/10.1016/j.jsc.2019.06.006. [doi:10.1016/j.jsc.2019.06.006](https://doi.org/10.1016/j.jsc.2019.06.006).
<a id="cite-holt-plesken"></a>
- **[HP89]** D.F. Holt and W. Plesken. *Perfect Groups*. Oxford University Press, 1989.
<a id="cite-hulpketrans"></a>
- **[Hul05]** Alexander Hulpke. Constructing transitive permutation groups. *J. Symbolic Comput.*, 39(1):1–30, 2005.
<a id="cite-kirschmer-symplectic"></a>
- **[Kir09]** M. Kirschmer. *Finite symplectic matrix groups*. Dissertation, RWTH Aachen, 2009. available at http://www.math.rwth-aachen.de/ Markus.Kirschmer/symplectic/thesis.pdf.
<a id="cite-newman-ob-vl-04"></a>
- **[MNVL04]** E.A. O'Brien M.F. Newman and M.R. Vaughan-Lee. Groups and nilpotent Lie rings whose order is the sixth power of a prime. *J. Algebra*, 278:383–401, 2004.
<a id="cite-nebe-ratgps-31"></a>
- **[Neb96]** G. Nebe. Finite subgroups of ${\rm GL}_n({\bf Q})$ for $25\leq n\leq 31$. *Comm. Algebra*, 24(7):2341–2397, 1996.
<a id="cite-nebe-quaternionic"></a>
- **[Neb98]** G. Nebe. Finite quaternionic matrix groups. *Represent. Theory*, 2:106–223, 1998.
<a id="cite-nebe-plesken-ratgps"></a>
- **[NP95]** G. Nebe and W. Plesken. Finite rational matrix groups. *Mem. Amer. Math. Soc.*, 1995.
<a id="cite-obrien-pgroup"></a>
- **[OBr90]** E.A. O'Brien. The $p$-group generation algorithm. *J. Symbolic Comput.*, 9:677–698, 1990.
<a id="cite-obrien-groups-256"></a>
- **[OBr91]** E.A. O'Brien. The Groups of Order 256. *J. Algebra*, 143:219–235, 1991.
<a id="cite-ob-vl-05"></a>
- **[OVL05]** E.A. O'Brien and M.R. Vaughan-Lee. The groups with order $p^7$ for odd prime $p$. *J. Algebra*, 2005.
<a id="cite-plesken-circulants"></a>
- **[Ple85]** Wilhelm Plesken. Finite unimodular groups of prime degree and circulants. *J. Algebra*, 97:286–312, 1985.
<a id="cite-pleskenpohst-glnz-i-ii"></a>
- **[PP77]** Wilhelm Plesken and Michael Pohst. On maximal finite irreducible subgroups of GL(n,Z). Parts I and II. *Math. Comp.*, 31:536–576, 1977.
<a id="cite-pleskenpohst-glnz-iii-v"></a>
- **[PP80]** Wilhelm Plesken and Michael Pohst. On maximal finite irreducible subgroups of GL(n,Z). Parts III-V. *Math. Comp.*, 34(149):245–301, 1980.
<a id="cite-prim2500"></a>
- **[RD05]** Colva M. Roney-Dougal. The primitive permutation groups of degree less than 2500. *J. Algebra*, 292(1):154–183, 2005.
<a id="cite-prim1000"></a>
- **[RDU03]** Colva M. Roney-Dougal and William R. Unger. The affine primitive permutation groups of degree less than 1000. *J. Symbolic Comp.*, 35:421–439, 2003.
<a id="cite-short"></a>
- **[Sho92]** Mark W. Short. *The Primitive Soluble Permutation Groups of Degree less than 256*. Volume 1519 of Lecture Notes in Math. Springer, Berlin and Heidelberg, 1992.
<a id="cite-sims-methods"></a>
- **[Sim70]** C.C. Sims. Computational methods in the study of permutation groups. In J. Leech, editor, *Computational problems in abstract algebra*, 169–183. Oxford - Pergamon, 1970.
<a id="cite-souvignier-gl8z-gl10z"></a>
- **[Sou94]** Bernd Souvignier. Irreducible finite integral matrix groups of degree 8 and 10. *Math. Comp.*, 63:335–350, 1994.