---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/FiniteGroups/MatrixGroupsOverGeneralRings/bibliography.html"
source: "https://docs.magma-maths.org/FiniteGroups/MatrixGroupsOverGeneralRings/bibliography.md"
part: "Finite Groups"
chapter: "Matrix Groups over General Rings"
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---

# Bibliography

<a id="cite-britnell-dphil"></a>
- **[Bri03]** John R. Britnell. *Cycle index methods for matrix groups over finite fields*. DPhil Thesis, University of Oxford, 2003.
<a id="cite-butler-schreier-matrix"></a>
- **[But76]** Gregory Butler. The Schreier Algorithm for Matrix Groups. In *Proceedings of SYMSAC '76*, 167–170. 1976.
<a id="cite-subgroups-permg"></a>
- **[CCH01b]** J.J. Cannon, B. Cox, and D.F. Holt. Computing the subgroups of a permutation group. *J. Symb. Comp.*, 31:149–161, 2001.
<a id="cite-autos-permg"></a>
- **[CH03]** J.J. Cannon and D.F. Holt. Automorphism group computation and isomorphism testing in finite groups. *J. Symbolic Comp.*, 35(3):241–267, 2003.
<a id="cite-chss-lix"></a>
- **[CHSS03]** J. Cannon, D. Holt, M. Slattery, A. Steel. “Computing subgroups of low index in a finite group.” 2003.
<a id="cite-clg-order"></a>
- **[CLG97b]** Frank Celler and Charles R. Leedham-Green. Calculating the Order of an Invertible Matrix. In Larry Finkelstein and William M. Kantor, editors, *Groups and Computation II*, volume 28 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 55–60. AMS, 1997.
<a id="cite-randomelements"></a>
- **[CLGM+95]** Frank Celler, Charles R. Leedham-Green, Scott H. Murray, Alice C. Niemeyer, and E. A. O'Brien. Generating random elements of a finite group. *Comm. Algebra*, 23(13):4931–4948, 1995.
<a id="cite-coutts-phd"></a>
- **[Cou11]** Hannah J. Coutts. *Topics in computational group theory: primitive permutation groups and matrix group normalisers*. PhD thesis, University of St Andrews, 2011.
<a id="cite-elo-auts"></a>
- **[ELGO02]** Bettina Eick, C.R. Leedham-Green, and E.A. O'Brien. Constructing automorphism groups of a $p$-groups. *Comm. Algebra*, 30:2271–2295, 2002.
<a id="cite-defranceschi-2018"></a>
- **[Fra18]** Giovanni De Franceschi. *Centralizers and conjugacy classes in finite classical groups*. PhD Thesis, University of Auckland, 2018.
<a id="cite-defranceschi-2020"></a>
- **[Fra20]** Giovanni De Franceschi. Centralizers and conjugacy classes in finite classical groups. *arXiv:2008.12651v1*, math.GR:69, 2020.
<a id="cite-dfol-classes"></a>
- **[FLO25]** Giovanni De Franceschi, Martin Liebeck, and E.A. O'Brien. *Conjugacy in finite classical groups*. Springer Mathematical Monographs. Springer, 2025.
<a id="cite-fulman-phd"></a>
- **[Ful97a]** Jason Fulman. *Probability in the Classical Groups over Finite Fields: Symmetric Functions, Stochastic Algorithms, and Cycle Indices*. PhD Thesis, Harvard University, 1997.
<a id="cite-gonshaw-etal-2017"></a>
- **[GLO17]** Samuel Gonshaw, Martin W. Liebeck, and E. A. O'Brien. Unipotent class representatives for finite classical groups. *J. Group Theory*, 20(3):505–525, 2017. URL: [https://doi.org/10.1515/jgth-2016-0047](https://doi.org/10.1515/jgth-2016-0047), [doi:10.1515/jgth-2016-0047](https://doi.org/10.1515/jgth-2016-0047).
<a id="cite-kl90"></a>
- **[KL90]** Peter Kleidman and Martin Liebeck. *The Subgroup Structure of the Finite Classical Groups*. Volume 129 of London Math. Soc. Lecture Note Ser. CUP, Cambridge, 1990. ISBN 0-521-35949-X.
<a id="cite-kuzpav2002"></a>
- **[KP02]** J. Kuzmanovich and A. Pavlichenkov. Finite groups of matrices whose entries are integers. *Amer. Math. Monthly*, 109(2):173–186, 2002.
<a id="cite-crlg-eaob"></a>
- **[LGO02]** C.R. Leedham-Green and E.A. O'Brien. Recognising tensor-induced matrix groups. *J. Algebra*, 253:14–30, 2002.
<a id="cite-grp-homs"></a>
- **[LGPS91]** C.R. Leedham-Green, C.E. Praeger, and L.H. Soicher. Computing with group homomorphisms. *J. Symbolic Comp.*, 12(4/5):527–532, 1991.
<a id="cite-mecky-neubuser"></a>
- **[MN89]** M. Mecky and J. Neubüser. Some remarks on the computation of conjugacy classes of soluble groups. *Bull. Austral, Math. Soc.*, 40(2):281–292, 1989.
<a id="cite-milnor-1969"></a>
- **[Mil69]** John Milnor. On isometries of inner product spaces. *Invent. Math.*, 8:83–97, 1969.
<a id="cite-minkwitz"></a>
- **[Min98]** Torsten Minkwitz. An algorithm for solving the factorization problem in permutation groups. *J. Symbolic Comput.*, 26(1):89–95, 1998. URL: [https://doi.org/10.1006/jsco.1998.0202](https://doi.org/10.1006/jsco.1998.0202), [doi:10.1006/jsco.1998.0202](https://doi.org/10.1006/jsco.1998.0202).
<a id="cite-murray-obrien"></a>
- **[MO95]** Scott H. Murray and E. A. O'Brien. Selecting base points for the Schreier-Sims algorithm for matrix groups. *J. Symbolic Comp.*, 6:577–584, 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-isglconjugate"></a>
- **[RD04]** Colva M. Roney-Dougal. Conjugacy of subgroups of the general linear group. *Experiment. Math.*, 13:151–163, 2004.
<a id="cite-schwingel-thesis"></a>
- **[Sch00b]** Ruth Schwingel. *Two matrix group algorithms with applications to computing the automorphism group of a finite $p$-group*. PhD thesis, Queen Mary and Westfield College, University of London, 2000.
<a id="cite-taylor-1992"></a>
- **[Tay92]** Donald E. Taylor. *The geometry of the classical groups*. Volume 9 of Sigma Series in Pure Mathematics. Heldermann Verlag, Berlin, 1992. ISBN 3-88538-009-9.
<a id="cite-chief-series-unger"></a>
- **[Ung]** W.R. Unger. Computing chief series of a large permutation group. In preparation.
<a id="cite-chtr-table-unger"></a>
- **[Ung06a]** W.R. Unger. Computing the character table of a finite group. *J. Symbolic Comp.*, 41(8):847–862, 2006.
<a id="cite-unger"></a>
- **[Ung06b]** W.R. Unger. Computing the solvable radical of a permutation group. *J. Algebra*, 300(1):305–315, 2006.
<a id="cite-wall-1963"></a>
- **[Wal63]** G. E. Wall. On the conjugacy classes in the unitary, symplectic and orthogonal groups. *J. Aust. Math. Soc.*, 3:1–62, 1963.