---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/FiniteGroups/MatrixGroupsOverFiniteFields/bibliography.html"
source: "https://docs.magma-maths.org/FiniteGroups/MatrixGroupsOverFiniteFields/bibliography.md"
part: "Finite Groups"
chapter: "Matrix Groups over Finite Fields"
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  - {"title": "Finite Groups", "source": "../index-finite-groups.md"}
  - {"title": "Matrix Groups over Finite Fields", "source": "index-matrix-groups-over-finite-fields.md"}
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---

# Bibliography

<a id="cite-ambroseetal"></a>
- **[AMPS10a]** S. Ambrose, S.H. Murray, C.E. Praeger, and C. Schneider. Constructive membership testing in black-box classical groups. In *Proceedings of The Third International Congress on Mathematical Software*, number 6327 in Lecture Notes in Computer Science, 54–57. Basel, 2010. Springer.
<a id="cite-asch-maximal-subgps"></a>
- **[Asc84]** M. Aschbacher. On the maximal subgroups of the finite classical groups. *Invent. Math*, 76:469–514, 1984.
<a id="cite-bray00"></a>
- **[Bra00]** J.N. Bray. An improved method of finding the centralizer of an involution. *Arch. Math. (Basel)*, 74(1):241–245, 2000.
<a id="cite-baarnhielmetal11"></a>
- **[BHLGO15]** H. Bäärnhielm, Derek Holt, C.R. Leedham-Green, and E.A. O'Brien. A practical model for computation with matrix groups. *J. Symbolic Comput.*, 68(68):27–60, 2015.
<a id="cite-cohenmurraytaylor"></a>
- **[CMT04]** Arjeh M. Cohen, Scott H. Murray, and D. E. Taylor. Computing in groups of Lie type. *Math. Comp.*, 73(247):1477–1498, 2004.
<a id="cite-cohen-taylor-preprint"></a>
- **[CT19]** Arjeh M. Cohen and D.E. Taylor. Row reduction for twisted groups of Lie type. *Preprint*, :, 2019.
<a id="cite-costi-phd"></a>
- **[Cos09]** E. Costi. *Constructive membership testing in classical groups*. PhD thesis, Queen Mary, University of London, 2009.
<a id="cite-dlgo-black"></a>
- **[DLGO15]** Heiko Dietrich, C.R. Leedham-Green, and E.A. O'Brien. Effective black-box constructive recognition of classical groups. *J. Algebra*, 460–492:421, 2015.
<a id="cite-dlgo-even"></a>
- **[DLLGO13]** Heiko Dietrich, Frank Lübeck, C.R. Leedham-Green, and E.A. O'Brien. Constructive recognition of classical groups in even characteristic. *J. Algebra*, 227–255:391, 2013.
<a id="cite-minimal-fields"></a>
- **[GH97]** S.P. Glasby and R.B. Howlett. Writing representations over minimal fields. *Comm. Algebra*, 25(6):1703–1711, 1997.
<a id="cite-glasby-lg-obrien"></a>
- **[GLGO05]** S.P. Glasby, C.R. Leedham-Green, and E.A. O'Brien. Writing projective representations over subfields. *J. Algebra*, 295():51–61, 2005.
<a id="cite-decomps-modules"></a>
- **[HLGOR96a]** Derek F. Holt, C.R. Leedham-Green, E.A. O'Brien, and Sarah Rees. Computing decompositions for modules with respect to a normal subgroup. *J. Algebra*, 184:818–838, 1996.
<a id="cite-matg-primitivity"></a>
- **[HLGOR96b]** Derek F. Holt, C.R. Leedham-Green, E.A. O'Brien, and Sarah Rees. Testing matrix groups for primitivity. *J. Algebra*, 184:795–817, 1996.
<a id="cite-howlett-rylands-taylor"></a>
- **[HRT01]** R. B. Howlett, L. J. Rylands, and D. E. Taylor. Matrix generators for exceptional groups of Lie type. *J. Symbolic Comput.*, 31(4):429–445, 2001.
<a id="cite-recog-tensor"></a>
- **[LGO97a]** C.R. Leedham-Green and E.A. O'Brien. Recognising tensor products of matrix groups. *Internat. J. Algebra Comput.*, 7:541–559, 1997.
<a id="cite-tp-pg"></a>
- **[LGO97b]** C.R. Leedham-Green and E.A. O'Brien. Tensor Products are Projective Geometries. *J. Algebra*, 189:514–528, 1997.
<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-lgo-odd"></a>
- **[LGO09]** C.R. Leedham-Green and E.A. O'Brien. Constructive recognition of classical groups in odd characteristic. *J. Algebra*, 322:833–881, 2009.
<a id="cite-lgo-pres"></a>
- **[LGO20]** C.R. Leedham-Green and E.A. O'Brien. Presentations on standard generators for classical groups. *J. Algebra*, 545:324–389, 2020.
<a id="cite-crlg01"></a>
- **[LG01]** Charles R. Leedham-Green. The computational matrix group project. In *Groups and computation, III (Columbus, OH, 1999)*, volume 8 of Ohio State Univ. Math. Res. Inst. Publ., pages 229–247. de Gruyter, Berlin, 2001.
<a id="cite-exceptional-lob16"></a>
- **[LO16]** Martin Liebeck and E.A. O'Brien. Recognition of finite exceptional groups of Lie type. *Trans. Amer. Math. Soc.*, 368:6189–6226, 2016.
<a id="cite-neunhoeffer-seress"></a>
- **[NS06]** Max Neunhöffer and Ákos Seress. A data structure for a uniform approach to computations with finite groups. In *ISSAC 2006*, pages 254–261. ACM, New York, 2006.
<a id="cite-niemeyer-normalisers"></a>
- **[Nie05]** Alice C. Niemeyer. Constructive recognition of normalisers of small extra-special matrix groups. *Internat. J. Algebra Comput.*, 15:367–394, 2005.
<a id="cite-obrien-survey"></a>
- **[OBr06]** E.A. O'Brien. Towards effective algorithms for linear groups. In *Finite Geometries, Groups and Computation*, volume of, 163–190. De Gruyer, 2006.
<a id="cite-obrien10"></a>
- **[OBr11]** E.A. O'Brien. Algorithms for matrix groups. In *Groups St Andrews (Bath)*, volume 388 of LMS Lecture Notes, 297–323. Cambridge University Press, 2011.