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<h3>References</h3>

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[<a href="https://www.ams.org/mathscinet-getitem?mr=1829468">AB01</a>] Altseimer, C. and Borovik, A. V.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=1676609">BB99</a>] Babai, L. and Beals, R.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=2780050">BBS09</a>] Babai, L., Beals, R. and Seress, Á.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=3283836">BHLO15</a>] Bäärnhielm, H., Holt, D., Leedham-Green, C. R. and O'Brien, E. A.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=1829473">BK01</a>] Brooksbank, P. A. and Kantor, W. M.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=2228648">BK06</a>] Brooksbank, P. A. and Kantor, W. M.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=1931364">BKPS02</a>] Babai, L., Kantor, W. M., Pálfy, P. P. and Seress, Á.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=1953539">BLN+03</a>] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=2166794">BLN+05</a>] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=1471984">BLS97</a>] Babai, L., Luks, E. M. and Seress, Á.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=2257997">BNS06</a>] Brooksbank, P., Niemeyer, A. C. and Seress, Á.,
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<a id="biBBro01" name="biBBro01"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1829472">Bro01</a>] Brooksbank, P. A.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=2051584">Bro03</a>] Brooksbank, P. A.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=2422320">Bro08</a>] Brooksbank, P. A.,
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<a id="biBBS01" name="biBBS01"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1829470">BS01</a>] Babai, L. and Shalev, A.,
Recognizing simplicity of black-box groups and the frequency
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<a id="biBCFL97" name="biBCFL97"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1444132">CFL97</a>] Cooperman, G., Finkelstein, L. and Linton, S.,
Constructive recognition of a black box group isomorphic to
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[<a href="https://www.ams.org/mathscinet-getitem?mr=1444130">CL97a</a>] Celler, F. and Leedham-Green, C. R.,
Calculating the order of an invertible matrix,
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<a id="biBCLG97b" name="biBCLG97b"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1444131">CL97b</a>] Celler, F. and Leedham-Green, C. R.,
A non-constructive recognition algorithm for the special
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<a id="biBCLG98" name="biBCLG98"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1647410">CL98</a>] Celler, F. and Leedham-Green, C. R.,
A constructive recognition algorithm for the special linear
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<a id="biBCLG01" name="biBCLG01"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1829474">CL01</a>] Conder, M. and Leedham-Green, C. R.,
Fast recognition of classical groups over large fields,
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<a id="biBCLGM+95" name="biBCLGM+95"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1356111">CLM+95</a>] Celler, F., Leedham-Green, C. R., Murray, S. H., Niemeyer, A. C. and O'Brien, E. A.,
Generating random elements of a finite group,
Comm. Algebra,
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<a id="biBCLGO06" name="biBCLGO06"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2187651">CLO06</a>] Conder, M. D. E., Leedham-Green, C. R. and O'Brien, E. A.,
Constructive recognition of PSL(2,q),
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<a id="biBCNRD09" name="biBCNRD09"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2531214">CNR09</a>] Carlson, J. F., Neunhöffer, M. and Roney-Dougal, C. M.,
A polynomial-time reduction algorithm for groups of semilinear
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J. Algebra,
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<a id="biBDLGLO13" name="biBDLGLO13"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3081630">DLLO13</a>] Dietrich, H., Leedham-Green, C. R., Lübeck, F. and O'Brien, E. A.,
Constructive recognition of classical groups in even
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<a id="biBDLGO15" name="biBDLGO15"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3272392">DLO15</a>] Dietrich, H., Leedham-Green, C. R. and O'Brien, E. A.,
Effective black-box constructive recognition of classical
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421
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<a id="biBGH97" name="biBGH97"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1446124">GH97</a>] Glasby, S. P. and Howlett, R. B.,
Writing representations over minimal fields,
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<a id="biBGLGO06" name="biBGLGO06"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2188850">GLO06</a>] Glasby, S. P., Leedham-Green, C. R. and O'Brien, E. A.,
Writing projective representations over subfields,
J. Algebra,
295 (1)
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<a id="biBHLO+08" name="biBHLO+08"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2466905">HLO+08</a>] Holmes, P. E., Linton, S. A., O'Brien, E. A., Ryba, A. J. E. and Wilson, R. A.,
Constructive membership in black-box groups,
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747–763 
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<a id="biBHLGOR96a" name="biBHLGOR96a"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1407872">HLOR96a</a>] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S.,
Computing matrix group decompositions with respect to a normal
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[<a href="https://www.ams.org/mathscinet-getitem?mr=1407871">HLOR96b</a>] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S.,
Testing matrix groups for primitivity,
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<a id="biBHR94" name="biBHR94"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1279282">HR94</a>] Holt, D. F. and Rees, S.,
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<a id="biBIL00" name="biBIL00"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1795309">IL00</a>] Ivanyos, G. and Lux, K.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=3085037">JLNP13</a>] Jambor, S., Leuner, M., Niemeyer, A. C. and Plesken, W.,
Fast recognition of alternating groups of unknown degree,
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<a id="biBKK15" name="biBKK15"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3272372">KK15</a>] Kantor, W. M. and Kassabov, M.,
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<a id="biBKM13" name="biBKM13"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3066774">KM13</a>] Kantor, W. M. and Magaard, K.,
Black box exceptional groups of Lie type,
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<a id="biBKM15" name="biBKM15"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3272395">KM15</a>] Kantor, W. M. and Magaard, K.,
Black box exceptional groups of Lie type II,
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421
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<a id="biBKS09" name="biBKS09"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2531224">KS09</a>] Kantor, W. M. and Seress, Á.,
Large element orders and the characteristic of Lie-type
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802–832 
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<a id="biBLG01" name="biBLG01"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1829483">Lee01</a>] Leedham-Green, C. R.,
The computational matrix group project,
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8
(2001),
229–247.


<a id="biBLMO07" name="biBLMO07"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2356848">LMO07</a>] Lübeck, F., Magaard, K. and O'Brien, E. A.,
Constructive recognition of SL_3(q),
J. Algebra,
316 (2)
(2007),
619–633 
(https://doi.org/10.1016/j.jalgebra.2007.01.020).


<a id="biBLNPS06" name="biBLNPS06"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2221258">LNPS06</a>] Law, M., Niemeyer, A. C., Praeger, C. E. and Seress, Á.,
A reduction algorithm for large-base primitive permutation
 groups,
LMS J. Comput. Math.,
9
(2006),
159–173 
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<a id="biBLGO97a" name="biBLGO97a"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1470352">LO97a</a>] Leedham-Green, C. R. and O'Brien, E. A.,
Recognising tensor products of matrix groups,
Internat. J. Algebra Comput.,
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(1997),
541–559 
(https://doi.org/10.1142/S0218196797000241).


<a id="biBLGO97b" name="biBLGO97b"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1438187">LO97b</a>] Leedham-Green, C. R. and O'Brien, E. A.,
Tensor products are projective geometries,
J. Algebra,
189 (2)
(1997),
514–528 
(https://doi.org/10.1006/jabr.1996.6881).


<a id="biBLGO02" name="biBLGO02"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1925006">LO02</a>] Leedham-Green, C. R. and O'Brien, E. A.,
Recognising tensor-induced matrix groups,
J. Algebra,
253 (1)
(2002),
14–30 
(https://doi.org/10.1016/S0021-8693(02)00041-8).


<a id="biBLO07" name="biBLO07"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2352733">LO07</a>] Liebeck, M. W. and O'Brien, E. A.,
Finding the characteristic of a group of Lie type,
J. Lond. Math. Soc. (2),
75 (3)
(2007),
741–754 
(https://doi.org/10.1112/jlms/jdm028).


<a id="biBLGO09" name="biBLGO09"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2531225">LO09</a>] Leedham-Green, C. R. and O'Brien, E. A.,
Constructive recognition of classical groups in odd
 characteristic,
J. Algebra,
322 (3)
(2009),
833–881 
(https://doi.org/10.1016/j.jalgebra.2009.04.028).


<a id="biBLO16" name="biBLO16"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3461031">LO16</a>] Liebeck, M. W. and O'Brien, E. A.,
Recognition of finite exceptional groups of Lie type,
Trans. Amer. Math. Soc.,
368 (9)
(2016),
6189–6226 
(https://doi.org/10.1090/tran/6534).


<a id="biBNeu09" name="biBNeu09"></a>

[Neu09] Neunhöffer, M.,
Constructive Recognition of Finite Groups,
Habilitation thesis,
RWTH Aachen
(2009) 
(https://github.com/neunhoef/habil).


<a id="biBNie05" name="biBNie05"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2142090">Nie05</a>] Niemeyer, A. C.,
Constructive recognition of normalizers of small extra-special
 matrix groups,
Internat. J. Algebra Comput.,
15 (2)
(2005),
367–394 
(https://doi.org/10.1142/S021819670500230X).


<a id="biBNP92" name="biBNP92"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1182102">NP92</a>] Neumann, P. M. and Praeger, C. E.,
A recognition algorithm for special linear groups,
Proc. London Math. Soc. (3),
65 (3)
(1992),
555–603 
(https://doi.org/10.1112/plms/s3-65.3.555).


<a id="biBNP97" name="biBNP97"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1444141">NP97</a>] Niemeyer, A. C. and Praeger, C. E.,
Implementing a recognition algorithm for classical groups,
 in Groups and computation, II (New Brunswick,
 NJ, 1995),
Amer. Math. Soc., Providence, RI,
DIMACS Ser. Discrete Math. Theoret. Comput. Sci.,
28
(1997),
273–296.


<a id="biBNP98" name="biBNP98"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1625479">NP98</a>] Niemeyer, A. C. and Praeger, C. E.,
A recognition algorithm for classical groups over finite
 fields,
Proc. London Math. Soc. (3),
77 (1)
(1998),
117–169 
(https://doi.org/10.1112/S0024611598000422).


<a id="biBNP99" name="biBNP99"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1717416">NP99</a>] Niemeyer, A. C. and Praeger, C. E.,
A recognition algorithm for non-generic classical groups over
 finite fields,
J. Austral. Math. Soc. Ser. A,
67 (2)
(1999),
223–253.


<a id="biBNS06" name="biBNS06"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=MR2289128">NS06</a>] Neunhöffer, M. and Seress, Á.,
A data structure for a uniform approach to computations with
 finite groups,
 in ISSAC 2006,
ACM,
New York
(2006),
254–261 
(https://doi.org/10.1145/1145768.1145811).


<a id="biBO'B06" name="biBO'B06"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2258009">O'B06] '>O'Brien, E. A.,
Towards effective algorithms for linear groups,
 in Finite geometries, groups, and computation,
Walter de Gruyter, Berlin
(2006),
163–190.


<a id="biBO'B11" name="biBO'B11"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2858866">O'B11] '>O'Brien, E. A.,
Algorithms for matrix groups,
 in Groups St Andrews 2009 in Bath.
 Volume 2,
Cambridge Univ. Press, Cambridge,
London Math. Soc. Lecture Note Ser.,
388
(2011),
297–323.


<a id="biBPak00" name="biBPak00"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1931844">Pak00</a>] Pak, I.,
The product replacement algorithm is polynomial,
 in 41st Annual Symposium on Foundations of
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 Science (Redondo Beach, CA, 2000),
IEEE Comput. Soc. Press, Los Alamitos, CA
(2000),
476–485 
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