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Bibliography

M. Aschbacher.
On the maximal subgroups of the finite classical groups.
Invent. Math, 76:469--514, 1984.

H. Baccent127aaccent127arnhielm.
Tensor decomposition of the Suzuki groups.
submitted, 2005.

H. Baccent127aaccent127arnhielm.
Recognising the Suzuki groups in their natural rep-re-sen-ta-tions.
J. Algebra, 300(1):171--198, 2006.

Baccent127aaccent127a14

H. Baccent127aaccent127arnhielm.
Recognising the Ree groups in their natural rep-re-sen-ta-tions.
J. Algebra, 416:139--166, 2014.

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.

BLGN+03

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.

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.

Car72

R. Carter.
Simple Groups of Lie Type.
John Wiley & Sons, London, New York, Sydney, Toronto, 1972.

CF64

R. Carter and P. Fong.
The Sylow 2-subgroups of the finite classical groups.
Journal of Algebra, 1:139--151, 1964.

CLG97a

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, pages 55--60. AMS, 1997.

CLG97b

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., pages 61--67. Amer. Math. Soc., 1997.

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.

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.

Cor13

Brian Corr.
Estimation and Computation with Matrices Over Finite Fields.
PhD thesis, University of Western Australia, 2013.

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.

HM01

G. Hiß and G. Malle.
Low-dimensional representations of quasi-simple groups.
LMS J. Comput. Math., 4:22--63, 2001.

HM02

G. Hiß and G. Malle.
Corrigenda: Low-dimensional representations of quasi-simple groups.
LMS J. Comput. Math., 5:95--126, 2002.

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.

Hur13

Barry Hurley.
Classification Problems for Finite Linear Groups.
PhD Thesis, National University of Ireland, 2013.

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.

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.

L"01

F. Lübeck.
Small degree representations of finite Chevalley groups in defining ch aracteristic.
LMS J. Comput. Math., 4:135--169, 2001.

LMO07

F Lübeck, K Magaard, and E.A. O'Brien.
Constructive recognition of SL₃(q).
J. Algebra, 2007:617--633, 2007.

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.

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.

NP92

Peter M. Neumann and Cheryl E. Praeger.
A Recognition Algorithm for Classical Groups.
Proc. London Math. Soc., 65(3):555--603, 1992.

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., pages 273--296. Amer. Math. Soc., 1997.

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.

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.

OW05

E.A. O'Brien and R.A. Wilson.
Subgroup chains in matrix groups.
preprint, 2005.

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, pages 605--623. Cambridge Univ. Press, 1999.

RD04

Colva M. Roney-Dougal.
Conjugacy of subgroups of the general linear group.
Experiment. Math., 13:151--163, 2004.

R.R57

R.Ree.
On some simple groups defined by Chevalley.
Trans. Am. Math. Soc., 84:392--400, 1957.

RT98

L.J. Rylands and D.E. Taylor.
Matrix generators for the orthogonal groups.
J. Symbolic Comp., 25:351--360, 1998.

Sta

M. Stather.
Constructive Sylow Theorems for the Classical Groups.
to appear in Journal of Algebra.

Tay87

Don Taylor.
Pairs of Generators for Matrix Groups. I.
Cayley Bulletin 3, 1987.

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.

V2.28, 13 July 2023