Robert A Wilson: publications

Recent Papers

• M. Neunhöffer, F. Noeske, E. A. O'Brien and R. A. Wilson, Orbit invariants and an application to the Baby Monster J. Algebra 341 (2011), 297-305.
• T. C. Burness, M. Giudici, R. A. Wilson, Prime order derangements in primitive permutation groups, J. Algebra 341 (2011), 158-178.
• Conway's group and octonions; R.A.Wilson. J. Group Theory 14 (2011), 1-8; doi: 10.1515/JGT.2010.038. Published online 13th August 2010.
• Another new approach to the small Ree groups; R.A.Wilson. Arch. Math. (Basel) 94 (2010), 501-510. The original publication is available at www.springerlink.com here.
• The Alperin weight conjecture and Uno's conjecture for the Monster M, p odd; Jianbei An and R.A. Wilson; LMS J. Comput. Math. 13 (2010), 320-356. Copyright held by the authors. Published by Cambridge Journals Online under non-exclusive licence.
• Recognising simplicity of black-box groups by constructing involutions and their centralisers; C.W.Parker and R.A.Wilson; J. Algebra 324 (2010), 885-915. The final published version can be found here.
• New computations in the Monster; R.A.Wilson; in `Moonshine - the first quarter century and beyond' (proceedings of Edinburgh conference, August 2004).
• Base sizes for sporadic simple groups; T.C.Burness, E.A.O'Brien and R.A.Wilson; Israel J. Math. 177 (2010) 307-333.
• An elementary construction of the Ree groups of type \({}^2G_2\); R.A.Wilson; Proc. Edinburgh Math. Soc. 53, (2010), 531-542.
• A new approach to the Suzuki groups; R.A.Wilson; Math. Proc. Cambridge Philos. Soc. 148 (2010), 425-428. doi:10.1017/S0305004109990399
  Copyright by Cambridge Philosophical Society, The published version can be found here.
• On the compact real form of the Lie algebra \(G_2\); R.A.Wilson; Math. Proc. Cambridge Philos. Soc. 148 (2010), 87-91. doi:10/1017/S030500410999020X
  Copyright by Cambridge Philosophical Society. The published version can be found here.
• A simple construction of the Ree groups of type \({}^2F_4\); R.A.Wilson; J. Algebra 323 (2010), 1468-1481. doi:10.16/j.jalgebra.2009.11.015.
  The published version is slightly different and can be found here.
• Octonions and the Leech lattice; R.A.Wilson; J. Algebra 322 (2009), 2186-2190 . The published version can be found here.
• Constructive membership in black-box groups; P.E. Holmes, S.A. Linton, E.A. O'Brien, A.J.E. Ryba, and R.A. Wilson; J. Group Theory 11 (2008), 747-763.
• Examples of 3-dimensional 1-cohomology for absolutely irreducible modules of finite simple groups; J.N.Bray, R.A.Wilson; J. Group Theory 11 (2008), 669-673.
• Enumerating big orbits and an application: B on the cosets of \(\mathrm{Fi_{23}}\); J. Müller, M. Neunhöffer, R.A.Wilson; J. Algebra (Computational Section), 314 (2007), 75-96.
• The character table of a maximal subgroup of the Monster; R. W. Barraclough, R. A. Wilson; LMS J. Comput. Math. 10 (2007), 161-175 (electronic). Supplementary material: Readme file, tar file. Copyright held by the authors. Published by Cambridge Journals Online under non-exclusive licence.
• Explicit construction of maximal subgroups of the Monster; J.N.Bray, R.A.Wilson; J. Algebra 300 (2006), 835-857.
• On the orders of automorphism groups of finite groups. II; J.N.Bray, R.A.Wilson; J. Group Theory 9 (2006), 537-545.
• Semi-presentations for sporadic simple groups; S.J.Nickerson, R.A.Wilson; Experimental Math. 14 (2005), 359-371. Supporting material is here as a gzipped tar file.
• Conjugacy class representatives in the Monster group; R.W.Barraclough, R.A.Wilson; LMS J. Comput. Math. 8 (2005), 205-216. Copyright held by the authors. Supplementary material: Readme file, tar file. Published by Cambridge Journals Online under non-exclusive licence.
• On the orders of automorphism groups of finite groups; J.N.Bray, R.A.Wilson; Bull. London Math. Soc. 37 (2005), 381-385.
• A characterization of finite soluble groups by laws in two variables; J.N.Bray, J.S.Wilson, R.A.Wilson. Bull. London Math. Soc. 37 (2005), 179-186.
• The Alperin weight conjecture and Uno's conjecture for the Baby Monster \(\mathbb B\), \(p\) odd; Jianbei An and R.A. Wilson; LMS J. Comput. Math. 7 (2004), 120-166. Copyright held by the authors. Published by Cambridge Journals Online under non-exclusive licence.

Reviews

• Klaus Lux and Herbert Pahlings, Group representations: a computational approach, reviewed in Bull. London Math. Soc., published online 8 July 2011.

Preprints

• R. A. Wilson, Some notes on the \(E_8\) lattice (6 pages).
• R. A. Wilson, Some notes on the groups \(F_4(q)\), \(E_6(q)\) and \({}^2E_6(q)\).
• R. A. Wilson, On the simple groups of Suzuki and Ree (25 pages).
• R. A. Wilson, A note on \(G_2(3)\), (4 pages).
• R. A. Wilson, On the compact real forms of the Lie algebras of type \(E_6\) and \(F_4\), (10 pages).
• R. A. Wilson, On the compact real form of the Lie group of type \(E_6\) and the triple cover of the orthogonal group \(\Omega_7(3)\), (9 pages).
• E. A. O'Brien, R. A. Wilson, Constructing stabilizer chains in matrix groups, in preparation.
• P. E. Holmes, R. A. Wilson, A Monster computer package in MAGMA, in preparation.
• The Sylow 2-subgroups of finite symmetric groups are rational; R.A.Wilson; (2004) preprint
  (withdrawn, as I discovered this result has already appeared in a paper by D.O.Revin, in Siberian Electronic Math. Reports (2004) at semr.math.nsc.ru)

Older papers

Expository and survey papers

• Maximal subgroups of sporadic groups, in Groups--St Andrews, 1985 (ed. Campbell and Robertson), 352-358. LMS Lecture Notes 121, Cambridge University Press.
• Construction of finite matrix groups, in Proceedings of the Euroconference on computational methods in representation theory, Essen, April 1997, 61-83. Progress in Math. 173. Birkhäuser, 1999.
• Computing in the Monster, in Groups, Combinatorics and Geometry--Durham 2001, pp. 327-335. World Scientific, 2003.

Research papers

1. The quaternionic lattice for \(2G_2(4)\) and its maximal subgroups, J. Algebra 77 (1982), 449-466.
2. The maximal subgroups of Conway's group \(\cdot 2\), J. Algebra 84 (1983), 107-114.
3. The complex Leech lattice and the maximal subgroups of the Suzuki group, J. Algebra 84 (1983), 151-188.
4. The maximal subgroups of Conway's group \(Co_1\), J. Algebra 85 (1983), 144-165.
5. The geometry and maximal subgroups of the simple groups of A. Rudvalis and J. Tits, Proc. London Math. Soc. (3) 48, (1984), 533-563.
6. On maximal subgroups of the Fischer group \(Fi_{22}\), Math. Proc. Cambridge Philos. Soc. 95 (1984), 197-222.
7. The subgroup structure of the Lyons group, Math. Proc. Cambridge Philos. Soc. 95 (1984), 403-409.
8. On lexicographic codes of minimal distance 4, Atti Sem. Mat. Fis. Univ. Modena 33 (1984), 125-135.
9. The maximal subgroups of the Lyons group, Math. Proc. Cambridge Philos. Soc. 97 (1985), 433-436.
10. Maximal subgroups of automorphism groups of simple groups, J. London Math. Soc. (2) 32 (1985), 460-466.
11. The maximal subgroups of the O'Nan group, J. Algebra 97 (1985), 467-473.
12. The geometry of the Hall-Janko group as a quaternionic reflection group, Geom. Dedicata 20 (1986), 157-173.
13. Is \(J_1\) a subgroup of the Monster? Bull. London. Math. Soc. 18 (1986), 349-350.
14. (with S. P. Norton) The maximal subgroups of the Harada-Norton group, J. Algebra 103 (1986), 362-376.
15. Some subgroups of the Baby Monster, Invent. Math. 89 (1987), 197-218.
16. The local subgroups of the Fischer groups, J. London Math. Soc. (2) 36 (1987), 77-94.
17. (with P. B. Kleidman) A characterization of some locally finite simple groups of Lie type, Arch. Math. 48 (1987), 10-14.
18. (with P. B. Kleidman) The maximal subgroups of \(Fi_{22}\), Math. Proc. Cambridge Philos. Soc. 102 (1987), 17-23. Corrigendum, ibid. 103 (1988), 383.
19. The odd-local subgroups of the Monster, J. Austral. Math. Soc. (A) 44 (1988), 1-16.
20. Some subgroups of the Thompson group, J. Austral. Math. Soc. (A) 44 (1988) 17-32.
21. On the 3-local subgroups of Conway's group \(Co_1\), J. Algebra 113 (1988), 261-262.
22. (with J. H. Conway and P. B. Kleidman) New families of ovoids in \(O_8^+\), Geom. Dedicata 26 (1988), 157-170.
23. (with P. B. Kleidman) The maximal subgroups of \(J_4\), Proc. London Math. Soc. (3) 56 (1988), 484-510.
24. (with P. B. Kleidman and R. A. Parker) The maximal subgroups of the Fischer group \(Fi_{23}\), J. London Math. Soc. (2) 39 (1989), 89-101.
25. Vector stabilizers and subgroups of Leech lattice groups, J. Algebra 127 (1989), 387-408.
26. (with S. P. Norton) The maximal subgroups of \(F_4(2)\) and its automorphism group, Comm. Algebra 17 (1989), 2809-2824.
27. (with P. B. Kleidman) The maximal subgroups of \(E_6(2)\) and \(\mathrm{Aut}(E_6(2))\), Proc. London Math. Soc. (3) 60 (1990), 266-294.
28. The 2- and 3- modular characters of \(J_3\), its covering group and automorphism group, J. Symbolic Comput. 10 (1990), 647-656.
29. (with R. A. Parker) The computer construction of matrix representations of finite groups over finite fields, J. Symbolic Comput. 9 (1990), 583-590.
30. (with P. B. Kleidman) \(J_3 < E_6(4)\) and \(M_{12} < E_6(5)\), J. London Math. Soc. (2) 42 (1990), 555-561.
31. (with S. A. Linton) The maximal subgroups of the Fischer groups \(Fi_{24}\) and \(Fi_{24}'\), Proc. London Math. Soc. (3) 63 (1991), 113-164.
32. (with I. A. I. Suleiman) Computer construction of matrix representations of the covering group of the Higman-Sims group, J. Algebra 148 (1992), 219-224.
33. (with I. A. I. Suleiman) The 3- and 5-modular characters of the covering and automorphism groups of the Higman-Sims group, J. Algebra 148 (1992), 225-242.
34. (with I. A. I. Suleiman) The 3-modular characters of the McLaughlin group McL and of its automorphism group McL:2, in Groups, Combinatorics and Geometry (ed. M.W. Liebeck and J. Saxl), LMS Lecture Notes 165 (1992), pp. 422-437.
35. (with M. D. E. Conder and A. J. Woldar) The symmetric genus of sporadic groups, Proc. Amer. Math. Soc. 116 (1992), 653-663.
36. Some new subgroups of the Baby Monster, Bull. London Math. Soc. 25 (1993), 23-28.
37. Matrix generators for Fischer's group \(Fi_{24}\), Math. Proc. Cambridge Philos. Soc. 113 (1993), 5-8.
38. The Brauer tree for \(J_3\) in characteristic 17, J. Symbolic Comput. 15 (1993), 325-330.
39. (with P. B. Kleidman) Sporadic simple subgroups of finite exceptional groups of Lie type, J. Algebra 157 (1993), 316-330.
40. A new construction of the Baby Monster, and its applications, Bull. London Math. Soc. 25 (1993), 431-437.
41. The symmetric genus of the Baby Monster, Quart. J. Math. (Oxford) 44 (1993), 513-516.
42. More on the maximal subgroups of the Baby Monster, Arch. Math. (Basel) 61 (1993), 497-507.
43. The action of a maximal parabolic subgroup on the transpositions of the Baby Monster, Proc. Edinburgh Math. Soc. 37 (1993), 185-189.
44. (with I. A. I. Suleiman) Construction of the fourfold cover of the Mathieu group \(M_{22}\), Experimental Math. 2 (1993), 11-14.
45. (with I. A. I. Suleiman) The 2-modular characters of Conway's second group \(Co_2\), Math. Proc. Cambridge Philos. Soc. 116 (1994), 275-283.
46. (with A. J. E. Ryba) Matrix generators for the Harada-Norton group, Experimental Math. 3 (1994), 137-145.
47. (with I. A. I. Suleiman) Standard generators for \(J_3\), Experimental Math. 4 (1995), 11-18.
48. (with C. Jansen) The minimal faithful 3-modular representation for the Lyons group, Comm. Algebra 24 (1996), 873-879.
49. Standard generators for sporadic simple groups, J. Algebra 184 (1996), 505-515.
50. The symmetric genus of the Fischer group \(Fi_{23}\), Topology 36 (1996), 379-380.
51. (with I. A. I. Suleiman) The 2-modular characters of Conway's third group \(Co_3\), J. Symbolic Comput. 24 (1997), 493-506.
52. (with C. Jansen) Two new constructions of the O'Nan group, J. London Math. Soc. 56 (1997), 579-583.
53. (with I. A. I. Suleiman), Covering and automorphism groups of \(U_6(2)\), Quart. J. Math. (Oxford) 48 (1997), 511-517.
54. (with C. Jansen) The 2-modular and 3-modular decomposition numbers for the sporadic simple O'Nan group and its triple cover, J. London Math. Soc. 57 (1998), 71-90.
55. An atlas of sporadic group representations, in The Atlas 10 years on (eds. R. T. Curtis and R. A. Wilson), pp. 261-273. LMS Lecture Note Series 249, Cambridge University Press, 1998.
56. A representation for the Lyons group in \(GL_{2480}(4)\), and a new uniqueness proof, Arch. Math. (Basel) 70 (1998), 11-15.
57. (with S. A. Linton, R. A. Parker and P. G. Walsh) Computer construction of the Monster, J. Group Theory 1 (1998), 307-337.
58. The McKay conjecture is true for the sporadic simple groups, J. Algebra 207 (1998), 294-305.
59. (with I. A. I. Suleiman), Construction of exceptional covers of generic groups, Math. Proc. Cambridge Philos. Soc. 125 (1999), 31-38.
60. The maximal subgroups of the Baby Monster, I, J. Algebra 211 (1999), 1-14.
61. (with J. Saxl and D. B. Wales), Embeddings of \(Sz(32)\) in \(E_8({\mathbb F})\), Bull. London Math. Soc. 32 (2000), 196-202.
62. (with R. A. Parker), Constructions of Fischer's Baby Monster over fields of characteristic not 2. J. Algebra 229 (2000), 109-117.
63. (with I. A. I. Suleiman and P. G. Walsh), Conjugacy classes in sporadic simple groups, Comm. Algebra 28 (2000), 3209-3222.
64. (with G. Havas and L. H. Soicher), A presentation for the Thompson sporadic simple group, pp. 193-200 in Groups and Computation III (eds. W. M. Kantor and A. Seress), Proceedings of the International Conference at the Ohio State University, June 15-19, 1999. W. de Gruyter, 2001.
65. (with J. N. Bray, I. A. I. Suleiman and P. G. Walsh), Generating maximal subgroups of sporadic simple groups, Comm. Algebra 29 (2001), 1325-1337.
66. The Monster is a Hurwitz group, J. Group Theory 4 (2001), 367-374.
67. (with S. P. Norton), Anatomy of the Monster, II, Proc. London Math. Soc. 84 (2002), 581-598.
68. (with P. E. Holmes), A new maximal subgroup of the Monster, J. Algebra 251 (2002), 435-447.
69. (with J. Müller, M. Neunhöffer and F. Röhr), Completing the Brauer trees for the sporadic simple Lyons group, London Math. Soc. J. Comput. Math. 5 (2002), 18-33.
70. Conjugacy class representatives in Fischer's Baby Monster, LMS JCM 5 (2002), 175-180.
71. (with P. E. Holmes), A new computer construction of the Monster using 2-local subgroups, J. London Math. Soc. 67 (2003), 349-364.
72. (with Jianbei An and E. A. O'Brien) The Alperin weight conjecture and Dade's conjecture for the simple group \(J_4\), LMS JCM 6 (2003), 119-140.
73. (with P. E. Holmes) \(PSL_2(59)\) is a subgroup of the Monster, J. London Math. Soc. 69 (2004), 141-152.