Group Theory

Computational Group Theory

20-04

  1. Sophie Ambrose, Matrix Groups: Theory, Algorithms and Applications, PhD Thesis, University of Western Australia, 2005.
  2. Sophie Ambrose, Max Neunhöffer, Cheryl E. Praeger, and Csaba Schneider, Generalised sifting in black-box groups, LMS J. Comput. Math. 8 (2005), 217–250 (electronic).[MR]
  3. Henrik Bäärnhielm, Recognising the Ree groups in their natural representations, Preprint (2006), 22 pages.[link]
  4. Henrik Bäärnhielm, Tensor decomposition of the Ree groups, Preprint (2006), 9 pages.[link]
  5. Henrik Bäärnhielm, Algorithmic problems in twisted groups of Lie type, preprint (2008), 131 pages.[arXiv]
  6. László Babai and Robert Beals, A polynomial-time theory of black box groups. I, Groups St. Andrews 1997 in Bath, I, London Math. Soc. Lecture Note Ser., vol. 260, Cambridge Univ. Press, Cambridge, 1999, pp. 30–64.[MR]
  7. László Babai and Igor Pak, Strong bias of group generators: An obstacle to the "product replacement algorithm", J. Algorithms 50 (2004), no. 2, 215–231.[MR]
  8. Hans Ulrich Besche and Bettina Eick, The groups of order at most 1000 except 512 and 768, J. Symbolic Comput. 27 (1999), no. 4, 405–413.[MR]
  9. Hans Ulrich Besche, Bettina Eick, and E. A. O'Brien, The groups of order at most 2000, Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 1–4 (electronic).[MR]
  10. Hans Ulrich Besche, Bettina Eick, and E. A. O'Brien, A millennium project: Constructing small groups, Internat. J. Algebra Comput. 12 (2002), no. 5, 623–644.[MR]
  11. Alexandre V. Borovik, Centralisers of involutions in black box groups, Computational and Statistical Group Theory (Las Vegas, NV/Hoboken, NJ, 2001), Contemp. Math., vol. 298, Amer. Math. Soc., Providence, RI, 2002, pp. 7–20.[MR]
  12. J. D. Bradley and R. T. Curtis, Symmetric generation and existence of McL : 2, the automorphism group of the McLaughlin group, Comm. Algebra 38 (2010), no. 2, 601–617.[MR/doi]
  13. John Bray, Marston Conder, Charles Leedham-Green, and Eamonn O'Brien, Short presentations for alternating and symmetric groups, Preprint (2006), 24 pages.
  14. John N. Bray and Robert T. Curtis, Double coset enumeration of symmetrically generated groups, J. Group Theory 7 (2004), no. 2, 167–185.[MR]
  15. Peter A. Brooksbank and William M. Kantor, Fast constructive recognition of black box orthogonal groups, J. Algebra 300 (2006), no. 1, 256–288.[MR]
  16. Peter A. Brooksbank and E. A. O'Brien, On intersections of classical groups, J. Group Theory 11 (2008), no. 4, 465–478.[MR]
  17. Ronald Brown, Neil Ghani, Anne Heyworth, and Christopher D. Wensley, String rewriting for double coset systems, J. Symbolic Comput. 41 (2006), no. 5, 573–590.[MR/arXiv]
  18. Timothy C. Burness, Martin W. Liebeck, and Aner Shalev, Base sizes for simple groups and a conjecture of Cameron, Proc. Lond. Math. Soc. (3) 98 (2009), no. 1, 116–162.[MR/doi]
  19. Timothy C. Burness, E. A. O'Brien, and Robert A. Wilson, Base sizes for sporadic simple groups, Israel J. Math., to appear (2008), 19 pages.
  20. G. Butler, S. S. Iyer, and E. A. O'Brien, A database of groups of prime-power order, Softw., Pract. Exper. 24 (1994), no. 10, 911-951.
  21. Colin M. Campbell, George Havas, and Edmund F. Robertson, Addendum to: "An elementary introduction to coset table methods in computational group theory", Groups—St. Andrews 1981, London Math. Soc. Lecture Note Ser., vol. 71, Cambridge Univ. Press, Cambridge, 2007, pp. 361–364.[MR]
  22. John J. Cannon, Bruce C. Cox, and Derek F. Holt, Computing Sylow subgroups in permutation groups, J. Symbolic Comput. 24 (1997), no. 3-4, 303–316.[MR]
  23. John J. Cannon, Bruce C. Cox, and Derek F. Holt, Computing the subgroups of a permutation group, J. Symbolic Comput. 31 (2001), no. 1-2, 149–161.[MR]
  24. John J. Cannon, Bettina Eick, and Charles R. Leedham-Green, Special polycyclic generating sequences for finite soluble groups, J. Symbolic Comput. 38 (2004), no. 5, 1445–1460.[MR]
  25. John Cannon and George Havas, Algorithms for groups, Australian Computer Journal 24 (1992), 51–60.
  26. John J. Cannon and Derek F. Holt, Computing chief series, composition series and socles in large permutation groups, J. Symbolic Comput. 24 (1997), no. 3-4, 285–301.[MR]
  27. John J. Cannon and Derek F. Holt, Automorphism group computation and isomorphism testing in finite groups, J. Symbolic Comput. 35 (2003), no. 3, 241–267.[MR]
  28. John J. Cannon and Derek F. Holt, Computing conjugacy class representatives in permutation groups, J. Algebra 300 (2006), no. 1, 213–222.[MR]
  29. John J. Cannon, Derek F. Holt, Michael Slattery, and Allan K. Steel, Computing subgroups of bounded index in a finite group, J. Symbol. Comput. 40 (2005), no. 2, 1013–1022.[MR]
  30. John Cannon and Bernd Souvignier, On the computation of conjugacy classes in permutation groups, in Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), ACM, New York, 1997, pp. 392–399 (electronic).[MR]
  31. Bill Casselman, Computation in Coxeter groups. II. Constructing minimal roots, Represent. Theory 12 (2008), 260–293.[MR]
  32. 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 (1995), no. 13, 4931–4948.[MR]
  33. Fokko du Cloux, The state of the art in the computation of Kazhdan-Lusztig polynomials, Appl. Algebra Engrg. Comm. Comput. 7 (1996), no. 3, 211–219.
  34. Arjeh M. Cohen, Sergei Haller, and Scott H. Murray, Computing in unipotent and reductive algebraic groups, LMS J. Comput. Math. 11 (2008), 343–366.[MR/arXiv]
  35. Arjeh M. Cohen, Sergei Haller, and Scott H. Murray, Computing with root subgroups of twisted reductive groups, preprint Submitted (2009).
  36. Arjeh M. Cohen, Scott H. Murray, and D. E. Taylor, Computing in groups of Lie type, Math. Comp. 73 (2004), no. 247, 1477–1498 (electronic).[MR]
  37. Marston Conder, Experimental algebra, Math. Chronicle 20 (1991), 1–11.[MR]
  38. Marston Conder and Peter Dobcsányi, Applications and adaptations of the low index subgroups procedure, Math. Comp. 74 (2005), no. 249, 485–497 (electronic).[MR]
  39. Marston Conder, C. R. Leedham-Green, and E. A. O'Brien, Constructive recognition of PSL(2,q), Trans. Amer. Math. Soc. 358 (2006), no. 3, 1203–1221 (electronic).[MR]
  40. Marston Conder and Charles R. Leedham-Green, Fast recognition of classical groups over large fields, Groups and Computation III (Columbus, OH, 1999), Ohio State Univ. Math. Res. Inst. Publ., vol. 8, de Gruyter, Berlin, 2001, pp. 113–121.[MR]
  41. Gene Cooperman, Larry Finkelstein, and Michael Tselman, Computing with matrix groups using permutation representations, in ISSAC '95: Proceedings of the 1995 international symposium on Symbolic and algebraic computation, ACM Press, New York, NY, USA, 1995, pp. 259–264.[doi]
  42. Gene Cooperman, Larry Finkelstein, Michael Tselman, and Bryant York, Constructing permutation representations for matrix groups, J. Symbolic Comput. 24 (1997), no. 3-4, 471–488.[MR]
  43. Gene Cooperman and Eric Robinson, Memory-based and disk-based algorithms for very high degree permutation groups, in ISSAC '03: Proceedings of the 2003 international symposium on Symbolic and algebraic computation, ACM Press, New York, NY, USA, 2003, pp. 66–73.[doi]
  44. A. S. Detinko and D. L. Flannery, On deciding finiteness of matrix groups, J. Symbolic Comput. 44 (2009), no. 8, 1037–1043.[MR]
  45. A. S. Detinko, D. L. Flannery, and E. A. O'Brien, Deciding finiteness of matrix groups in positive characteristic, J. Algebra 322 (2009), no. 11, 4151–4160.[MR/doi]
  46. Bettina Eick, Computational group theory, Jahresber. Deutsch. Math.-Verein. 107 (2005), no. 3, 155–170.[MR/link]
  47. Bettina Eick, C. R. Leedham-Green, and E. A. O'Brien, Constructing automorphism groups of p-groups, Comm. Algebra 30 (2002), no. 5, 2271–2295.[MR]
  48. Bettina Eick and E. A. O'Brien, Enumerating p-groups, J. Austral. Math. Soc. Ser. A 67 (1999), no. 2, 191–205.[MR]
  49. Arash Farzan and J. Ian Munro, Succinct representation of finite abelian groups, in ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computation, ACM Press, New York, NY, USA, 2006, pp. 87–92.[doi]
  50. Claus Fieker, Minimizing representations over number fields, J. Symbolic Comput. 38 (2004), no. 1, 833–842.[MR]
  51. Claus Fieker and Jürgen Klüners, Minimal discriminants for fields with small Frobenius groups as Galois groups, J. Number Theory 99 (2003), no. 2, 318–337.[MR]
  52. Volker Gebhardt, Constructing a short defining set of relations for a finite group, J. Algebra 233 (2000), no. 2, 526–542.[MR]
  53. Volker Gebhardt, Efficient collection in infinite polycyclic groups, J. Symbolic Comput. 34 (2002), no. 3, 213–228.[MR]
  54. Volker Gebhardt, A new approach to the conjugacy problem in Garside groups, J. Algebra 292 (2005), no. 1, 282–302.[MR]
  55. Volker Gebhardt, Conjugacy search in braid groups: From a braid-based cryptography point of view, Appl. Algebra Engrg. Comm. Comput. 17 (2006), no. 3-4, 219–238.[MR]
  56. S. P. Glasby, C. R. Leedham-Green, and E. A. O'Brien, Writing projective representations over subfields, J. Algebra 295 (2006), no. 1, 51–61.[MR]
  57. S. P. Glasby and Cheryl E. Praeger, Towards an efficient Meat-axe algorithm using f-cyclic matrices: the density of uncyclic matrices in M(n,q), J. Algebra 322 (2009), no. 3, 766–790.
  58. Anja Groch, Dennis Hofheinz, and Rainer Steinwandt, A practical attack on the root problem in braid groups, Algebraic methods in cryptography, Contemp. Math., vol. 418, Amer. Math. Soc., Providence, RI, 2006, pp. 121–131.[MR/link]
  59. R. Haas and A. G. Helminck, Algorithms for twisted involutions in Weyl groups, Preprint (2006), 10 pages.
  60. George Havas, Coset enumeration strategies, Watt, Stephen M. (ed.), ISSAC '91. Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation. Bonn, Germany, July 15–17, 1991. New York, NY: ACM Press, 1991, pp. 191–199.
  61. George Havas, C. R. Leedham-Green, E. A. O'Brien, and Michael C. Slattery, Computing with elation groups, Finite Geometries, Groups, and Computation, Walter de Gruyter GmbH &Co. KG, Berlin, 2006, pp. 95–102.[MR]
  62. George Havas, M. F. Newman, Alice C. Niemeyer, and Charles C. Sims, Computing in groups with exponent six, Computational and Geometric Aspects of Modern Algebra, London Math. Soc. Lecture Note Ser., vol. 275, Cambridge Univ. Press, Cambridge, 1998, pp. 87–100.
  63. George Havas and Colin Ramsay, Proving a group trivial made easy: A case study in coset enumeration, Bull. Austral. Math. Soc. 62 (2000), no. 1, 105–118.[MR]
  64. George Havas and Colin Ramsay, On proofs in finitely presented groups, Groups St. Andrews 2005. Vol. 2, London Math. Soc. Lecture Note Ser., vol. 340, Cambridge Univ. Press, Cambridge, 2007, pp. 457–474.[MR]
  65. George Havas and Edmund F. Robertson, Application of computational tools for finitely presented groups, Computational support for discrete mathematics (Piscataway, NJ, 1992), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 15, Amer. Math. Soc., Providence, RI, 1994, pp. 29–39.[MR]
  66. George Havas, Edmund F. Robertson, and Dale C. Sutherland, Behind and beyond a theorem on groups related to trivalent graphs, J. Aust. Math. Soc. 85 (2008), no. 3, 323–332.
  67. George Havas and M. R. Vaughan-Lee, Computing with 4-Engel groups, Groups St. Andrews 2005. Vol. 2, London Math. Soc. Lecture Note Ser., vol. 340, Cambridge Univ. Press, Cambridge, 2007, pp. 475–485.[MR]
  68. George Havas and Michael Vaughan-Lee, On counterexamples to the Hughes conjecture, J. Algebra 322 (2009), no. 3, 791–801.
  69. P. E. Holmes, S. A. Linton, E. A. O'Brien, A. J. E. Ryba, and R. A. Wilson, Constructive membership in black-box groups, J. Group Theory 11 (2008), no. 6, 747–763.[MR]
  70. D. F. Holt, The computation of normalizers in permutation groups, J. Symbolic Comput. 12 (1991), no. 4-5, 499–516.[MR]
  71. Derek F. Holt, The Meataxe as a tool in computational group theory, The Atlas of Finite Groups: Ten Years On (Birmingham, 1995), London Math. Soc. Lecture Note Ser., vol. 249, Cambridge Univ. Press, Cambridge, 1998, pp. 74–81.[MR]
  72. Derek F. Holt, Computing automorphism groups of finite groups, Groups and Computation, III (Columbus, OH, 1999), Ohio State Univ. Math. Res. Inst. Publ., vol. 8, de Gruyter, Berlin, 2001, pp. 201–208.[MR]
  73. Derek F. Holt, Cohomology and group extensions in Magma, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 221–241.[MR]
  74. Derek F. Holt, Bettina Eick, and Eamonn A. O'Brien, Handbook of Computational Group Theory, Discrete Mathematics and its Applications (Boca Raton), Chapman &Hall/CRC, Boca Raton, FL, 2005, pp. xvi+514.[MR]
  75. Derek F. Holt, C. R. Leedham-Green, E. A. O'Brien, and Sarah Rees, Computing matrix group decompositions with respect to a normal subgroup, J. Algebra 184 (1996), no. 3, 818–838.[MR]
  76. Derek F. Holt, C. R. Leedham-Green, E. A. O'Brien, and Sarah Rees, Testing matrix groups for primitivity, J. Algebra 184 (1996), no. 3, 795–817.[MR]
  77. Derek F. Holt and E. A. O'Brien, A computer-assisted analysis of some matrix groups, J. Algebra 300 (2006), no. 1, 199–212.[MR]
  78. Derek F. Holt and Mark J. Stather, Computing a chief series and the soluble radical of a matrix group over a finite field, LMS J. Comput. Math. 11 (2008), 223–251.[MR]
  79. Alexander Hulpke, Computing subgroups invariant under a set of automorphisms, J. Symbolic Comput. 27 (1999), no. 4, 415–427.[MR]
  80. Alexander Hulpke, Representing subgroups of finitely presented groups by quotient subgroups, Experiment. Math. 10 (2001), no. 3, 369–381.[MR]
  81. Alexander Hulpke, Constructing transitive permutation groups, J. Symbolic Comput. 39 (2005), no. 1, 1–30.[MR]
  82. Stephen P. Humphries, Generators for the mapping class group, Topology of low-dimensional manifolds (Proc. Second Sussex Conf., Chelwood Gate, 1977), Lecture Notes in Math., vol. 722, Springer, Berlin, 1979, pp. 44–47.[MR]
  83. Stephen P. Humphries and Kenneth W. Johnson, Fusions of character tables II. p-groups, Comm. Algebra 37 (2009), no. 12, 4296–4315.[MR/doi]
  84. William M. Kantor, Sylow's theorem in polynomial time, J. Comput. System Sci. 30 (1985), no. 3, 359–394.[MR]
  85. William M. Kantor, Simple groups in computational group theory, in Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 1998, pp. 77–86 (electronic).[MR]
  86. William M. Kantor and Ákos Seress, Black box classical groups, Mem. Amer. Math. Soc. 149 (2001), no. 708, viii+168.[MR]
  87. Boris Kunyavskii, Eugene Plotkin, and Roman Shklyar, A strategy for human-computer study of equations and identities in finite groups, Proc. Latv. Acad. Sci. Sect. B Nat. Exact Appl. Sci. 57 (2003), no. 3-4, 97–101.[MR]
  88. Rudolf Land, Computation of Pólya polynomials of primitive permutation groups, Math. Comp. 36 (1981), no. 153, 267–278.[MR]
  89. R. Laue, Construction of groups and the constructive approach to group actions, Symmetry and Structural Properties of Condensed Matter (Zajolhk Aczkowo, 1994), World Sci. Publishing, River Edge, NJ, 1995, pp. 404–416.[MR]
  90. Reinhard Laue, Computing double coset representatives for the generation of solvable groups, Computer algebra (Marseille, 1982), Lecture Notes in Comput. Sci., vol. 144, Springer, Berlin, 1982, pp. 65–70.[MR]
  91. C. R. Leedham-Green and Scott H. Murray, Variants of product replacement, Computational and Statistical Group Theory (Las Vegas, NV/Hoboken, NJ, 2001), Contemp. Math., vol. 298, Amer. Math. Soc., Providence, RI, 2002, pp. 97–104.[MR]
  92. C. R. Leedham-Green and E. A. O'Brien, Recognising tensor-induced matrix groups, J. Algebra 253 (2002), no. 1, 14–30.[MR]
  93. C. R. Leedham-Green and E. A. O'Brien, Constructive recognition of classical groups in odd characteristic, J. Algebra 322 (2009), no. 3, 833–881.[MR/doi]
  94. Charles R. Leedham-Green, The computational matrix group project, Groups and Computation III (Columbus, OH, 1999), Ohio State Univ. Math. Res. Inst. Publ., vol. 8, de Gruyter, Berlin, 2001, pp. 229–247.[MR]
  95. Martin W. Liebeck and E. A. O'Brien, Finding the characteristic of a group of Lie type, J. Lond. Math. Soc. (2) 75 (2007), no. 3, 741–754.[MR]
  96. Eddie H. Lo, A polycyclic quotient algorithm, J. Symbolic Comput. 25 (1998), no. 1, 61–97.[MR]
  97. Andrea Lucchini and Federico Menegazzo, Computing a set of generators of minimal cardinality in a solvable group, J. Symbolic Comput. 17 (1994), no. 5, 409–420.[MR]
  98. Eugene M. Luks and Pierre McKenzie, Parallel algorithms for solvable permutation groups, J. Comput. System Sci. 37 (1988), no. 1, 39–62.[MR]
  99. Eugene M. Luks and Takunari Miyazaki, Polynomial-time normalizers for permutation groups with restricted composition factors, in ISSAC '02: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2002, pp. 176–183 (electronic).[MR/link]
  100. Eugene M. Luks, Ferenc Rákóczi, and Charles R. B. Wright, Computing normalizers in permutation p-groups, in ISSAC '94: Proceedings of the international symposium on Symbolic and algebraic computation, ACM Press, New York, NY, USA, 1994, pp. 139–146.[doi]
  101. Eugene M. Luks, Ferenc Rákóczi, and Charles R. B. Wright, Some algorithms for nilpotent permutation groups, J. Symbolic Comput. 23 (1997), no. 4, 335–354.[MR]
  102. Klaus M. Lux and Magdolna Szőke, Computing homomorphism spaces between modules over finite dimensional algebras, Experiment. Math. 12 (2003), no. 1, 91–98.[MR]
  103. Kay Magaard, Sergey Shpectorov, and Helmut Völklein, A GAP package for braid orbit computation and applications, Experiment. Math. 12 (2003), no. 4, 385–393.[MR]
  104. Gerhard O. Michler, An algorithm for determining the simplicity of a modular group representation, J. Symbolic Comput. 6 (1988), no. 1, 105–111.[MR]
  105. Gerhard O. Michler, Some problems in computational representation theory, J. Symbolic Comput. 9 (1990), no. 5-6, 571–582.[MR]
  106. Torsten Minkwitz, On the computation of ordinary irreducible representations of finite groups, ISSAC '95: Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 1995, pp. 278–284.
  107. Takunari Miyazaki, Polynomial-time computation in matrix groups, PhD Thesis, University of Oregon, 1999.
  108. Meinard Müller and Michael Clausen, DFT-based word normalization in finite supersolvable groups, Appl. Algebra Engrg. Comm. Comput. 15 (2004), no. 3-4, 213–231.[MR/doi]
  109. Scott H. Murray and E. A. O'Brien, Selecting base points for the Schreier-Sims algorithm for matrix groups, J. Symbolic Comput. 19 (1995), no. 6, 577–584.[MR]
  110. J. Neubüser, An invitation to computational group theory, Groups '93 Galway/St. Andrews, Vol. 2, London Math. Soc. Lecture Note Ser., vol. 212, Cambridge Univ. Press, Cambridge, 1995, pp. 457–475.[MR]
  111. Peter M. Neumann and Cheryl E. Praeger, Cyclic matrices and the MEATAXE, Groups and Computation, III (Columbus, OH, 1999), Ohio State Univ. Math. Res. Inst. Publ., vol. 8, de Gruyter, Berlin, 2001, pp. 291–300.[MR]
  112. Max Neunhöffer and Ákos Seress, A data structure for a uniform approach to computations with finite groups, ISSAC'06: Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2006, pp. 254–261.[MR/doi]
  113. M. F. Newman, Addendum: "A computer aided study of a group defined by fourth powers" (Bull. Austral. Math. Soc. 14 (1976), no. 2, 293–297), Bull. Austral. Math. Soc. 15 (1976), no. 3, 477–479.[MR]
  114. M. F. Newman, Some group presentations and enforcing the associative law, Algebraic algorithms and error correcting codes (Grenoble, 1985), Lecture Notes in Comput. Sci., vol. 229, Springer, Berlin, 1986, pp. 228–237.[MR]
  115. M. F. Newman, Werner Nickel, and Alice C. Niemeyer, Descriptions of groups of prime-power order, J. Symbolic Comput. 25 (1998), no. 5, 665–682.[MR]
  116. M. F. Newman and E. A. O'Brien, A CAYLEY library for the groups of order dividing 128, Group Theory (Singapore, 1987), de Gruyter, Berlin, 1989, pp. 437–442.[MR]
  117. M. F. Newman and E. A. O'Brien, A computer-aided analysis of some finitely presented groups, J. Austral. Math. Soc. Ser. A 53 (1992), no. 3, 369–376.[MR]
  118. M. F. Newman and E. A. O'Brien, Application of computers to questions like those of Burnside. II, Internat. J. Algebra Comput. 6 (1996), no. 5, 593–605.[MR]
  119. M. F. Newman and E. A. O'Brien, Classifying 2-groups by coclass, Trans. Amer. Math. Soc. 351 (1999), no. 1, 131–169.[MR]
  120. Alice C. Niemeyer, A finite soluble quotient algorithm, J. Symbolic Comput. 18 (1994), no. 6, 541–561.[MR]
  121. Alice C. Niemeyer, Computing finite soluble quotients, Computational Algebra and Number Theory (Sydney, 1992), Math. Appl., vol. 325, Kluwer Acad. Publ., Dordrecht, 1995, pp. 75–82.[MR]
  122. Alice C. Niemeyer, Constructive recognition of normalizers of small extra-special matrix groups, Internat. J. Algebra Comput. 15 (2005), no. 2, 367–394.[MR]
  123. Alice C. Niemeyer and Cheryl E. Praeger, A recognition algorithm for classical groups over finite fields, Proc. London Math. Soc. (3) 77 (1998), no. 1, 117–169.[MR]
  124. E. A. O'Brien, The p-group generation algorithm, J. Symbolic Comput. 9 (1990), no. 5-6, 677–698.[MR]
  125. E. A. O'Brien, Isomorphism testing for p-groups, J. Symbolic Comput. 17 (1994), no. 2, 131, 133–147.[MR]
  126. E. A. O'Brien, Computing automorphism groups of p-groups, Computational Algebra and Number Theory (Sydney, 1992), Math. Appl., vol. 325, Kluwer Acad. Publ., Dordrecht, 1995, pp. 83–90.[MR]
  127. E. A. O'Brien, Towards effective algorithms for linear groups, Finite Geometries, Groups, and Computation, Walter de Gruyter GmbH &Co. KG, Berlin, 2006, pp. 163–190.[MR]
  128. E. A. O'Brien and M. R. Vaughan-Lee, The groups with order p7 for odd prime p, J. Algebra 292 (2005), no. 1, 243–258.[MR]
  129. Igor Pak, The product replacement algorithm is polynomial, 41st Annual Symposium on Foundations of Computer Science (Redondo Beach, CA, 2000), IEEE Comput. Soc. Press, Los Alamitos, CA, 2000, pp. 476–485.[MR]
  130. Igor Pak, What do we know about the product replacement algorithm?, Groups and Computation, III (Columbus, OH, 1999), Ohio State Univ. Math. Res. Inst. Publ., vol. 8, de Gruyter, Berlin, 2001, pp. 301–347.[MR]
  131. Andrea Previtali, Irreducible constituents of monomial representations, J. Symbolic Comput. 41 (2006), no. 12, 1345–1359.[MR]
  132. Birgit Reinert and Dirk Zeckzer, Coset enumeration using prefix Gröbner bases: an experimental approach, LMS J. Comput. Math. 4 (2001), 74–134 (electronic).[MR/link]
  133. Eric Robinson and Gene Cooperman, A parallel architecture for disk-based computing over the baby monster and other large finite simple groups, in ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computation, ACM Press, New York, NY, USA, 2006, pp. 298–305.[doi]
  134. Eric Robinson, Jürgen Müller, and Gene Cooperman, A disk-based parallel implementation for direct condensation of large permutation modules, ISSAC 2007, ACM, New York, 2007, pp. 315–322.[MR]
  135. Colva M. Roney-Dougal, Conjugacy of subgroups of the general linear group, Experiment. Math. 13 (2004), no. 2, 151–163.[MR]
  136. Colva M. Roney-Dougal and William R. Unger, Computing the primitive permutation groups of degree less than 1000, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 243–260.[MR]
  137. Mohamed Sayed, Coset enumeration of groups generated by symmetric sets of involutions, Int. J. Math. Math. Sci. (2005), no. 23, 3739–3750.[MR]
  138. Mohamed Sayed, Double-coset enumeration algorithm for symmetrically generated groups, Int. J. Math. Math. Sci. (2005), no. 5, 699–715.[MR]
  139. Mohamed Sayed, Combinatorial method in the coset enumeration of symmetrically generated groups, Int. J. Comput. Math. 85 (2008), no. 7, 993–1001.[MR]
  140. Gerhard J. A. Schneider, Computing with endomorphism rings of modular representations, J. Symbolic Comput. 9 (1990), no. 5-6, 607–636.[MR]
  141. Ákos Seress, An introduction to computational group theory, Notices Amer. Math. Soc. 44 (1997), no. 6, 671–679.[MR]
  142. Ákos Seress, Nearly linear time algorithms for permutation groups: an interplay between theory and practice, Acta Appl. Math. 52 (1998), no. 1-3, 183–207.[MR]
  143. Ákos Seress, A unified approach to computations with permutation and matrix groups, International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 245–258.[MR]
  144. Charles C. Sims, Computing with subgroups of automorphism groups of finite groups, in ISSAC '97: Proceedings of the 1997 international symposium on Symbolic and algebraic computation, ACM Press, New York, NY, USA, 1997, pp. 400–403.[doi]
  145. Michael C. Slattery, Computing character degrees in p-groups, J. Symbolic Comput. 2 (1986), no. 1, 51–58.[MR]
  146. Michael C. Slattery, Computing double cosets in soluble groups, J. Symbolic Comput. 31 (2001), no. 1-2, 179–192.[MR]
  147. Leonard H. Soicher, Computing with graphs and groups, Topics in algebraic graph theory, Encyclopedia of Mathematics and its Applications, vol. 102, Cambridge University Press, Cambridge, 2004, pp. 250–266.[MR]
  148. Bernd Souvignier, Decomposing homogeneous modules of finite groups in characteristic zero, J. Algebra 322 (2009), no. 3, 948–956.
  149. P. Christopher Staecker, Computing twisted conjugacy classes in free groups using nilpotent quotients, preprint (2007), 14 pages.[arXiv]
  150. Polina Strogova, Finding a finite group presentation using rewriting, Symbolic Rewriting Techniques (Ascona, 1995), Progr. Comput. Sci. Appl. Logic, vol. 15, Birkhäuser, Basel, 1998, pp. 267–276.[MR]
  151. Gernot Stroth, Algorithms in pure mathematics, Computational discrete mathematics, Lecture Notes in Comput. Sci., vol. 2122, Springer, Berlin, 2001, pp. 148–158.[MR]
  152. W. R. Unger, Computing the character table of a finite group, J. Symbolic Comput. 41 (2006), no. 8, 847–862.[MR]
  153. W. R. Unger, Computing the soluble radical of a permutation group, J. Algebra 300 (2006), no. 1, 305–315.[MR]
  154. N. A. Vavilov, V. I. Mysovskikh, and Yu. G. Teterin, Computational group theory in St. Petersburg, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 236 (1997), no. Vopr. Teor. Predst. Algebr i Grupp. 5, 42–49, 215–216.[MR]
  155. Katsushi Waki, Calculation of direct summands of FG-modules, Sci. Rep. Hirosaki Univ. 44 (1997), no. 2, 193–200.[MR]
  156. Michael Weller, Konstruktion der konjugiertenklassen von untergruppen mit kleinem index in p-gruppen, PhD Thesis, Universität-Gesamthochschule-Essen, 1993.
  157. Michael Weller, Construction of classes of subgroups of small index in p-groups, Arch. Math. (Basel) 68 (1997), no. 2, 89–99.[MR]