# Robert A Wilson: publications

This page: Recent Papers | Preprints | Older papers || External links: Books | Lecture notes | Grant reports

## Recent Papers (from 2010)

For copyright reasons, links to copies of the papers held on this server are usually to preprint versions. The final published versions can be found on the relevant journal's website.
1. R.A. Wilson, Classification of subgroups isomorphic to $$PSL_2(27)$$ in the Monster, LMS JCM 17 (2014), 33-46. A preprint version, which is slightly different, is available at arxiv.org/abs/1304.5338
2. L. Babai, S. Guest, C. Praeger and R. Wilson, Proportions of $$r$$-regular elements in classical groups, J. London Math. Soc., 88 (2013), 202-226, arxiv.org/abs/1205.1327/ doi:10.1112/jlms/jdt011
3. R. A. Wilson, On the simple groups of Suzuki and Ree Proc. London Math. Soc. 107 (2013), 680-712. doi: 10.1112/plms/pds091
4. A. Farooq, S.P. Norton and R. A. Wilson, A presentation of the Monster and a set of matrices which satisfy it, J. Algebra 379 (2013), 432-440. Final published version: http://dx.doi.org/10.1016/j.jalgebra.2013.01.015
5. S. P. Norton and R. A. Wilson, A correction to the $41$-structure of the Monster, a construction of a new maximal subgroup $$\mathrm{L}_2(41)$$, and a new moonshine phenomenon, J. London Math. Soc. 87 (2013), 943-962. doi: 10.1112/jlms/jds078 Final published version.
6. R. A. Wilson, On the compact real forms of the Lie algebras of type $$E_6$$ and $$F_4$$, Siberian Math. J. 54 (2013), 159-172. DOI: 10.1134/S0037446613010011. arxiv.org/abs/1208.3967
7. K. Magaard and R. A. Wilson, Algorithmic construction of Chevalley bases, LMS JCM, 15 (2012) 436-443. arxiv.org/abs/1203.5228. Copyright by the authors. Published under non-exclusive licence.
8. R. A. Wilson, On a 14-dimensional lattice invariant under the simple group $$G_2(3)$$, J. Group Theory, 15 (2012), 709-717 (published online 7/7/12).
9. 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.
10. T. C. Burness, M. Giudici, R. A. Wilson, Prime order derangements in primitive permutation groups, J. Algebra 341 (2011), 158-178.
11. 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.
12. 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.
13. 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.
14. 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.
15. New computations in the Monster; R.A.Wilson; in `Moonshine - the first quarter century and beyond' (proceedings of Edinburgh conference, August 2004).
16. Base sizes for sporadic simple groups; T.C.Burness, E.A.O'Brien and R.A.Wilson; Israel J. Math. 177 (2010) 307-333.
17. An elementary construction of the Ree groups of type $${}^2G_2$$; R.A.Wilson; Proc. Edinburgh Math. Soc. 53, (2010), 531-542.
18. 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.
19. 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.
20. 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.

## Preprints

Some more preprints will be added shortly. Email me if you want any of them urgently.
1. Tevian Dray, Corinne A. Manogue and Robert A. Wilson, A symplectic representation of $$\mathrm E_7$$, arxiv.org/abs/1311.0341
2. R. A. Wilson, Albert algebras and construction of the finite simple groups $$F_4(q)$$, $$E_6(q)$$ and $${}^2E_6(q)$$ and their generic covers, arxiv.org/abs/1310.5886
3. R.A. Wilson, The Monster and black-box groups, arxiv.org/abs/1310.5016
4. R.A. Wilson, An explicit embedding of the Tits group in the compact real form of $$E_6$$, arxiv.org/abs/1208.4221
5. R. A. Wilson, A quaternionic construction of $$E_7$$ (12 pages), to appear in Proc. Amer. Math. Soc.
6. R. A. Wilson, Some notes on the $$E_8$$ lattice (6 pages).
7. 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).
8. E. A. O'Brien, R. A. Wilson, Constructing stabilizer chains in matrix groups, in preparation.
9. P. E. Holmes, R. A. Wilson, A Monster computer package in MAGMA, in preparation.
10. 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 (1982-2009)

### 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.
74. 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.
75. 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.
76. 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.
77. On the orders of automorphism groups of finite groups; J.N.Bray, R.A.Wilson; Bull. London Math. Soc. 37 (2005), 381-385.
78. 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.
79. Explicit construction of maximal subgroups of the Monster; J.N.Bray, R.A.Wilson; J. Algebra 300 (2006), 835-857.
80. On the orders of automorphism groups of finite groups. II; J.N.Bray, R.A.Wilson; J. Group Theory 9 (2006), 537-545.
81. 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.
82. 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.
83. On subgroups of the Monster containing $$A_5$$s; P.E. Holmes and R. A. Wilson; J. Algebra 319 (2008), 2653-2667.
84. 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.
85. 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.
86. Octonions and the Leech lattice; R.A.Wilson; J. Algebra 322 (2009), 2186-2190 . The published version can be found here.

This page is maintained by Robert Wilson. Last updated 22 October 2013.