[AB01] Altseimer, C. and Borovik, A. V., Probabilistic recognition of orthogonal and symplectic groups, in Groups and computation, III (Columbus, OH, 1999), de Gruyter, Berlin, 8 (2001), 1–20.
[BB99] Babai, L. and Beals, R., A polynomial-time theory of black box groups. I, in Groups St. Andrews 1997 in Bath, I, Cambridge Univ. Press, Cambridge, London Math. Soc. Lecture Note Ser., 260 (1999), 30–64.
[BBS09] Babai, L., Beals, R. and Seress, Á., Polynomial-time theory of matrix groups, in STOC'09–-Proceedings of the 2009 ACM International Symposium on Theory of Computing, ACM, New York (2009), 55–64.
[BHLO15] Bäärnhielm, H., Holt, D., Leedham-Green, C. R. and O'Brien, E. A.,
A practical model for computation with matrix groups,
J. Symbolic Comput.,
68 (part 1)
(2015),
27–60
(https://doi.org/10.1016/j.jsc.2014.08.006).
[BK01] Brooksbank, P. A. and Kantor, W. M., On constructive recognition of a black box \({\rm PSL}(d,q)\), in Groups and computation, III (Columbus, OH, 1999), de Gruyter, Berlin, Ohio State Univ. Math. Res. Inst. Publ., 8 (2001), 95–111.
[BK06] Brooksbank, P. A. and Kantor, W. M.,
Fast constructive recognition of black box orthogonal groups,
J. Algebra,
300 (1)
(2006),
256–288
(https://doi.org/10.1016/j.jalgebra.2006.02.024).
[BKPS02] Babai, L., Kantor, W. M., Pálfy, P. P. and Seress, Á.,
Black-box recognition of finite simple groups of Lie type by
statistics of element orders,
J. Group Theory,
5 (4)
(2002),
383–401
(https://doi.org/10.1515/jgth.2002.010).
[BLN+03] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á.,
A black-box group algorithm for recognizing finite symmetric
and alternating groups. I,
Trans. Amer. Math. Soc.,
355 (5)
(2003),
2097–2113
(https://doi.org/10.1090/S0002-9947-03-03040-X).
[BLN+05] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á.,
Constructive recognition of finite alternating and symmetric
groups acting as matrix groups on their natural permutation
modules,
J. Algebra,
292 (1)
(2005),
4–46
(https://doi.org/10.1016/j.jalgebra.2005.01.035).
[BLS97] Babai, L., Luks, E. M. and Seress, Á.,
Fast management of permutation groups. I,
SIAM J. Comput.,
26 (5)
(1997),
1310–1342
(https://doi.org/10.1137/S0097539794229417).
[BNS06] Brooksbank, P., Niemeyer, A. C. and Seress, Á., A reduction algorithm for matrix groups with an extraspecial normal subgroup, in Finite geometries, groups, and computation, Walter de Gruyter, Berlin (2006), 1–16.
[Bro01] Brooksbank, P. A., A constructive recognition algorithm for the matrix group \(\Omega(d,q)\), in Groups and computation, III (Columbus, OH, 1999), de Gruyter, Berlin, Ohio State Univ. Math. Res. Inst. Publ., 8 (2001), 79–93.
[Bro03] Brooksbank, P. A.,
Fast constructive recognition of black-box unitary groups,
LMS J. Comput. Math.,
6
(2003),
162–197
(https://doi.org/10.1112/S1461157000000437).
[Bro08] Brooksbank, P. A.,
Fast constructive recognition of black box symplectic groups,
J. Algebra,
320 (2)
(2008),
885–909
(https://doi.org/10.1016/j.jalgebra.2008.03.021).
[BS01] Babai, L. and Shalev, A., Recognizing simplicity of black-box groups and the frequency of \(p\)-singular elements in affine groups, in Groups and computation, III (Columbus, OH, 1999), de Gruyter, Berlin, Ohio State Univ. Math. Res. Inst. Publ., 8 (2001), 39–62.
[CFL97] Cooperman, G., Finkelstein, L. and Linton, S., Constructive recognition of a black box group isomorphic to \({\rm GL}(n,2)\), in Groups and computation, II (New Brunswick, NJ, 1995), Amer. Math. Soc., Providence, RI, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 28 (1997), 85–100.
[CL97a] Celler, F. and Leedham-Green, C. R., Calculating the order of an invertible matrix, in Groups and computation, II (New Brunswick, NJ, 1995), Amer. Math. Soc., Providence, RI, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 28 (1997), 55–60.
[CL97b] Celler, F. and Leedham-Green, C. R., A non-constructive recognition algorithm for the special linear and other 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), 61–67.
[CL98] Celler, F. and Leedham-Green, C. R.,
A constructive recognition algorithm for the special linear
group,
in The atlas of finite groups: ten years on (Birmingham,
1995),
Cambridge Univ. Press, Cambridge,
London Math. Soc. Lecture Note Ser.,
249
(1998),
11–26
(https://doi.org/10.1017/CBO9780511565830.007).
[CL01] Conder, M. and Leedham-Green, C. R., Fast recognition of classical groups over large fields, in Groups and computation, III (Columbus, OH, 1999), de Gruyter, Berlin, Ohio State Univ. Math. Res. Inst. Publ., 8 (2001), 113–121.
[CLM+95] 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,
23 (13)
(1995),
4931–4948
(https://doi.org/10.1080/00927879508825509).
[CLO06] Conder, M. D. E., Leedham-Green, C. R. and O'Brien, E. A.,
Constructive recognition of \({\rm PSL}(2,q)\),
Trans. Amer. Math. Soc.,
358 (3)
(2006),
1203–1221
(https://doi.org/10.1090/S0002-9947-05-03756-6).
[CNR09] Carlson, J. F., Neunhöffer, M. and Roney-Dougal, C. M.,
A polynomial-time reduction algorithm for groups of semilinear
or subfield class,
J. Algebra,
322 (3)
(2009),
613–637
(https://doi.org/10.1016/j.jalgebra.2009.04.022).
[DLLO13] Dietrich, H., Leedham-Green, C. R., Lübeck, F. and O'Brien, E. A.,
Constructive recognition of classical groups in even
characteristic,
J. Algebra,
391
(2013),
227–255
(https://doi.org/10.1016/j.jalgebra.2013.04.031).
[DLO15] Dietrich, H., Leedham-Green, C. R. and O'Brien, E. A.,
Effective black-box constructive recognition of classical
groups,
J. Algebra,
421
(2015),
460–492
(https://doi.org/10.1016/j.jalgebra.2014.08.039).
[GH97] Glasby, S. P. and Howlett, R. B.,
Writing representations over minimal fields,
Comm. Algebra,
25 (6)
(1997),
1703–1711
(https://doi.org/10.1080/00927879708825947).
[GLO06] Glasby, S. P., Leedham-Green, C. R. and O'Brien, E. A.,
Writing projective representations over subfields,
J. Algebra,
295 (1)
(2006),
51–61
(https://doi.org/10.1016/j.jalgebra.2005.03.037).
[HLO+08] Holmes, P. E., Linton, S. A., O'Brien, E. A., Ryba, A. J. E. and Wilson, R. A.,
Constructive membership in black-box groups,
J. Group Theory,
11 (6)
(2008),
747–763
(https://doi.org/10.1515/JGT.2008.047).
[HLOR96a] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S.,
Computing matrix group decompositions with respect to a normal
subgroup,
J. Algebra,
184 (3)
(1996),
818–838
(https://doi.org/10.1006/jabr.1996.0286).
[HLOR96b] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S.,
Testing matrix groups for primitivity,
J. Algebra,
184 (3)
(1996),
795–817
(https://doi.org/10.1006/jabr.1996.0285).
[HR94] Holt, D. F. and Rees, S., Testing modules for irreducibility, J. Austral. Math. Soc. Ser. A, 57 (1) (1994), 1–16.
[IL00] Ivanyos, G. and Lux, K.,
Treating the exceptional cases of the MeatAxe,
Experiment. Math.,
9 (3)
(2000),
373–381
(http://projecteuclid.org/euclid.em/1045604672).
[JLNP13] Jambor, S., Leuner, M., Niemeyer, A. C. and Plesken, W.,
Fast recognition of alternating groups of unknown degree,
J. Algebra,
392
(2013),
315–335
(https://doi.org/10.1016/j.jalgebra.2013.06.005).
[KK15] Kantor, W. M. and Kassabov, M.,
Black box groups isomorphic to \(\rm {PGL}(2,2^e)\),
J. Algebra,
421
(2015),
16–26
(https://doi.org/10.1016/j.jalgebra.2014.08.014).
[KM13] Kantor, W. M. and Magaard, K.,
Black box exceptional groups of Lie type,
Trans. Amer. Math. Soc.,
365 (9)
(2013),
4895–4931
(https://doi.org/10.1090/S0002-9947-2013-05822-9).
[KM15] Kantor, W. M. and Magaard, K.,
Black box exceptional groups of Lie type II,
J. Algebra,
421
(2015),
524–540
(https://doi.org/10.1016/j.jalgebra.2014.09.003).
[KS09] Kantor, W. M. and Seress, Á.,
Large element orders and the characteristic of Lie-type
simple groups,
J. Algebra,
322 (3)
(2009),
802–832
(https://doi.org/10.1016/j.jalgebra.2009.05.004).
[Lee01] Leedham-Green, C. R., The computational matrix group project, in Groups and computation, III (Columbus, OH, 1999), de Gruyter, Berlin, Ohio State Univ. Math. Res. Inst. Publ., 8 (2001), 229–247.
[LMO07] Lübeck, F., Magaard, K. and O'Brien, E. A.,
Constructive recognition of \({\rm SL}_3(q)\),
J. Algebra,
316 (2)
(2007),
619–633
(https://doi.org/10.1016/j.jalgebra.2007.01.020).
[LNPS06] 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
(https://doi.org/10.1112/S1461157000001236).
[LO97a] Leedham-Green, C. R. and O'Brien, E. A.,
Recognising tensor products of matrix groups,
Internat. J. Algebra Comput.,
7 (5)
(1997),
541–559
(https://doi.org/10.1142/S0218196797000241).
[LO97b] 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).
[LO02] 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).
[LO07] 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).
[LO09] 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).
[LO16] 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).
[Neu09] Neunhöffer, M.,
Constructive Recognition of Finite Groups,
Habilitation thesis,
RWTH Aachen
(2009)
(https://github.com/neunhoef/habil).
[Nie05] 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).
[NP92] 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).
[NP97] 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.
[NP98] 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).
[NP99] 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.
[NS06] 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).
[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.
[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.
[Pak00] Pak, I.,
The product replacement algorithm is polynomial,
in 41st Annual Symposium on Foundations of
Computer
Science (Redondo Beach, CA, 2000),
IEEE Comput. Soc. Press, Los Alamitos, CA
(2000),
476–485
(https://doi.org/10.1109/SFCS.2000.892135).
[Par84] Parker, R. A., The computer calculation of modular characters (the meat-axe), in Computational group theory (Durham, 1982), Academic Press, London (1984), 267–274.
[Pra99] Praeger, C. E.,
Primitive prime divisor elements in finite classical groups,
in Groups St. Andrews 1997 in Bath,
II,
Cambridge Univ. Press, Cambridge,
London Math. Soc. Lecture Note Ser.,
261
(1999),
605–623
(https://doi.org/10.1017/CBO9780511666148.024).
[Ser03] Seress, Á.,
Permutation group algorithms,
Cambridge University Press, Cambridge,
Cambridge Tracts in Mathematics,
152
(2003),
x+264 pages
(https://doi.org/10.1017/CBO9780511546549).
generated by GAPDoc2HTML