---
title: "Bibliography"
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---

# Bibliography

<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-bkps"></a>
- **[BKPS02]** L. Babai, W. M. Kantor, P. P. Pálfy, and Á. Seress. Black-box recognition of finite simple groups of Lie type by statistics of element orders. *J. Group Theory*, 5:383–401, 2002.
<a id="cite-altsymrecog1"></a>
- **[BLGN+03b]** R. Beals, C. R. Leedham-Green, A. C. Niemeyer, C. E. Praeger, and A. Seress. A black-box algorithm for recognising finite symmetric and alternating groups, I. *Trans. Amer. Math. Soc.*, pages 2097–2113, 2003.
<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-sz-tensor-decompose"></a>
- **[Baa05]** H. Bäärnhielm. Tensor decomposition of the Suzuki groups. submitted, 2005.
<a id="cite-baarnhielm05"></a>
- **[Baa06a]** H. Bäärnhielm. Recognising the Suzuki groups in their natural representations. *J. Algebra*, 300(1):171–198, 2006.
<a id="cite-baarnhielm14"></a>
- **[Baa14]** H. Bäärnhielm. Recognising the Ree groups in their natural representations. *J. Algebra*, 416:139–166, 2014.
<a id="cite-car72"></a>
- **[Car72a]** R. Carter. *Simple Groups of Lie Type*. John Wiley & Sons, London, New York, Sydney, Toronto, 1972.
<a id="cite-caf64"></a>
- **[CF64]** R. Carter and P. Fong. The Sylow 2-subgroups of the finite classical groups. *Journal of Algebra*, 1:139–151, 1964.
<a id="cite-clg-recog"></a>
- **[CLG97a]** Frank Celler and C.R. Leedham-Green. A non-constructive recognition algorithm for the special linear and other classical groups. In *Groups and computation II (New Brunswick, NJ, 1995)*, volume 28 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 61–67. Amer. Math. Soc., 1997.
<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-conder-lg-obrien"></a>
- **[CLGO06]** M.D.E. Conder, C.R. Leedham-Green, and E.A. O'Brien. Constructive recognition for $PSL(2, q)$. *Trans. Amer. Math. Soc.*, 358():1203–1221, 2006.
<a id="cite-corr-phd"></a>
- **[Cor13]** Brian Corr. *Estimation and Computation with Matrices Over Finite Fields*. PhD thesis, University of Western Australia, 2013.
<a id="cite-flannery-obrien"></a>
- **[FO05]** D.L. Flannery and E.A. O'Brien. Linear groups of small degree over finite fields. *Internat. J. Algebra and Comput.*, 15:467–502, 2005.
<a id="cite-hiss-malle"></a>
- **[HM01]** G. Hiß and G. Malle. Low-dimensional representations of quasi-simple groups. *LMS J. Comput. Math.*, 4:22–63, 2001.
<a id="cite-hiss-malle-c"></a>
- **[HM02]** G. Hiß and G. Malle. Corrigenda: Low-dimensional representations of quasi-simple groups. *LMS J. Comput. Math.*, 5:95–126, 2002.
<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-hurley-phd"></a>
- **[Hur13]** Barry Hurley. *Classification Problems for Finite Linear Groups*. PhD Thesis, National University of Ireland, 2013.
<a id="cite-altsymrecogn"></a>
- **[JLNP13]** S Jambor, M Leuner, A. C. Niemeyer, and W Plesken. Fast recognition of alternating groups of unknown degree. *J. Algebra*, 392:315–335, 2013.
<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-luebeck"></a>
- **[Lub01]** F. Lübeck. Small degree representations of finite Chevalley groups in defining ch aracteristic. *LMS J. Comput. Math.*, 4:135–169, 2001.
<a id="cite-liebeck-obrien"></a>
- **[LO07]** Martin Liebeck and E.A. O'Brien. Finding the characteristic of a group of Lie type. *J. London Math. Soc.*, 75():741–754, 2007.
<a id="cite-lubeck-magaard-obrien"></a>
- **[LMO07]** F Lübeck, K Magaard, and E.A. O'Brien. Constructive recognition of $\SL_3(q)$. *J. Algebra*, 2007:617–633, 2007.
<a id="cite-maas"></a>
- **[Maa09]** Lukas Maas. On a construction of the basic spin representations of symmetric groups. https://arxiv.org/abs/0911.3794, 2009.
<a id="cite-small-deg-reps"></a>
- **[MOAS08]** Kay Magaard, E. A. O'Brien, and Ákos Seress. Recognition of small dimensional representations of general linear groups. *J. Austral. Math. Soc.*, 85:229–250, 2008.
<a id="cite-neumann-praeger-92"></a>
- **[NP92]** Peter M. Neumann and Cheryl E. Praeger. A Recognition Algorithm for Classical Groups. *Proc. London Math. Soc.*, 65(3):555–603, 1992.
<a id="cite-niemeyer-praeger-97"></a>
- **[NP97]** Alice C. Niemeyer and Cheryl E. Praeger. Implementing a Recognition Algorithm for Classical Groups. In *Groups and computation II (New Brunswick, NJ, 1995)*, volume 28 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 273–296. Amer. Math. Soc., 1997.
<a id="cite-niemeyer-praeger-98"></a>
- **[NP98]** Alice C. Niemeyer and Cheryl E. Praeger. A Recognition Algorithm for Classical Groups over Finite Fields. *Proc. London Math. Soc.*, 77(3):117–169, 1998.
<a id="cite-niemeyer-praeger-99"></a>
- **[NP99]** Alice C. Niemeyer and Cheryl E. Praeger. A Recognition Algorithm for Non-Generic Classical Groups over Finite Fields. *J. Austral. Math. Soc. Ser. A*, 67:223–253, 1999.
<a id="cite-obrien-wilson"></a>
- **[OW05]** E.A. O'Brien and R.A. Wilson. Subgroup chains in matrix groups. *preprint*, ():, 2005.
<a id="cite-praeger-prim"></a>
- **[Pra99]** Cheryl E. Praeger. Primitive prime divisor elements in finite classical groups. In *Proc. of Groups St. Andrews 1997 in Bath II*, number 261 in London Math. Soc. Lecture Notes Series, 605–623. Cambridge Univ. Press, 1999.
<a id="cite-ree57"></a>
- **[RRe57]** R.Ree. On some simple groups defined by Chevalley. *Trans. Am. Math. Soc.*, 84:392–400, 1957.
<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-rylands-taylor"></a>
- **[RT98]** L.J. Rylands and D.E. Taylor. Matrix generators for the orthogonal groups. *J. Symbolic Comp.*, 25:351–360, 1998.
<a id="cite-stather"></a>
- **[Sta]** M. Stather. Constructive Sylow Theorems for the Classical Groups. to appear in Journal of Algebra.
<a id="cite-taylor"></a>
- **[Tay87]** Don Taylor. Pairs of Generators for Matrix Groups. I. *Cayley Bulletin 3*, 1987.
<a id="cite-we55"></a>
- **[Wei55]** A. Weir. Sylow p-subgroups of the classical groups over finite fields with characteristic prime to p. *Proc. Am. Math. Soc*, 6:529–533, 1955.