GAP (recog) - References

Goto Chapter: Top 1 2 3 4 5 6 7 8 9 Bib Ind
[Top of Book] [Contents] [Previous Chapter] [Next Chapter]

[MathJax on]

### References

[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.

[BHLGO15] 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 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).

[BLGN+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).

[BLGN+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 Ω(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 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.

[CLG97a] 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.

[CLG97b] 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.

[CLG98] 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).

[CLG01] 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.

[CLGM+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).

[CLGO06] Conder, M. D. E., Leedham-Green, C. R. and O'Brien, E. A., Constructive recognition of PSL(2,q), Trans. Amer. Math. Soc., 358 (3) (2006), 1203–1221
(https://doi.org/10.1090/S0002-9947-05-03756-6).

[CNRD09] 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).

[DLGLO13] 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).

[DLGO15] 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).

[GLGO06] 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).

[HLGOR96a] 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).

[HLGOR96b] 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).

[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).

[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 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).

[LG01] 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.

[LGO97a] 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).

[LGO97b] 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).

[LGO02] 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).

[LGO09] 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).

[LMO07] 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).

[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).

[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).

[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).

[Top of Book] [Contents] [Previous Chapter] [Next Chapter]
Goto Chapter: Top 1 2 3 4 5 6 7 8 9 Bib Ind

generated by GAPDoc2HTML