Robert A Wilson: publications
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.
 Robert A. Wilson, Is Sz(8) a subgroup of the Monster?,
Bull. London Math. Soc. 48 (2016), 355364.
Abstract
Full Text
PDF.
 Robert A. Wilson, Every \(PSL_2(13)\) in the Monster contains \(13A\)elements,
Preprint, 22nd January 2015. The published version, which is different,
appears in the LMS JCM, vol 18 (2015), 667674. (Copyright held by the author.)
 Tevian Dray, Corinne A. Manogue and Robert A. Wilson,
A symplectic representation of \(\mathrm E_7\), Comment. Math. Univ. Carolin. 55 (2014), no. 3, 387–399.
arxiv.org/abs/1311.0341
 R. A. Wilson, A quaternionic construction of \(E_7\),
Proc. Amer. Math. Soc. 142 (2014), no. 3, 867–880.
 R.A. Wilson, Classification of subgroups isomorphic to
\(PSL_2(27)\) in the Monster, LMS JCM 17 (2014), 3346. A preprint version, which is slightly different, is available at
arxiv.org/abs/1304.5338
 L. Babai, S. Guest, C. Praeger and R. Wilson,
Proportions of \(r\)regular elements in classical groups,
J. London Math. Soc., 88 (2013), 202226, arxiv.org/abs/1205.1327/ doi:10.1112/jlms/jdt011
 R. A. Wilson, On the simple groups of Suzuki and Ree
Proc. London Math. Soc. 107 (2013), 680712. doi: 10.1112/plms/pds091
 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), 432440.
Final published version: http://dx.doi.org/10.1016/j.jalgebra.2013.01.015
 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), 943962. doi: 10.1112/jlms/jds078
Final published version.
 R. A. Wilson, On the compact real forms of the Lie algebras of type \(E_6\) and \(F_4\),
Siberian Math. J. 54 (2013), 159172.
DOI: 10.1134/S0037446613010011.
arxiv.org/abs/1208.3967
 K. Magaard and R. A. Wilson, Algorithmic construction of Chevalley bases,
LMS JCM, 15 (2012) 436443.
arxiv.org/abs/1203.5228.
Copyright by the authors. Published under nonexclusive licence.
 R. A. Wilson, On a 14dimensional lattice invariant under
the simple group \(G_2(3)\),
J. Group Theory, 15 (2012), 709717 (published online 7/7/12).
 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), 297305.
 T. C. Burness, M. Giudici, R. A. Wilson,
Prime order derangements in primitive permutation groups, J. Algebra 341 (2011), 158178.

Conway's group and octonions; R.A.Wilson.
J. Group Theory 14 (2011), 18; 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), 501510. 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), 320356. Copyright held by the authors.
Published by Cambridge Journals Online
under nonexclusive licence.

Recognising simplicity of blackbox groups by constructing
involutions and their centralisers;
C.W.Parker and R.A.Wilson; J. Algebra 324 (2010), 885915. 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) 307333.

An elementary construction of the Ree groups of type \({}^2G_2\);
R.A.Wilson;
Proc. Edinburgh Math. Soc. 53, (2010), 531542.

A new approach to the Suzuki groups; R.A.Wilson; Math. Proc. Cambridge Philos. Soc.
148 (2010), 425428.
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), 8791.
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), 14681481. doi:10.16/j.jalgebra.2009.11.015.
The published version is slightly different and can be found
here.
Some more preprints will be added shortly. Email me if you want any of them urgently.
 John N. Bray, Richard A. Parker and Robert A. Wilson,
Finding 47:23 in the Baby Monster,
revised version, November 2015, to appear in LMS JCM.
 Robert A. Wilson, There is no Sz(8) in the Monster, Preprint, 19th August 2015.
revised version.
arxiv.org/abs/1508.04996
 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
 R.A. Wilson, The Monster and blackbox groups,
arxiv.org/abs/1310.5016
 R.A. Wilson, An explicit embedding of the Tits group in the compact real
form of \(E_6\), arxiv.org/abs/1208.4221
 R. A. Wilson, Some notes on the \(E_8\) lattice (6 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 2subgroups 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)
Expository and survey papers
 Maximal subgroups of sporadic groups, in GroupsSt Andrews, 1985 (ed.
Campbell
and Robertson), 352358.
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, 6183. Progress in Math. 173. Birkhäuser, 1999.
 Computing in the Monster, in Groups, Combinatorics and
GeometryDurham 2001, pp. 327335. World Scientific, 2003.
Research papers
 The quaternionic lattice for \(2G_2(4)\) and its maximal subgroups,
J. Algebra 77 (1982), 449466.
 The maximal subgroups of Conway's group \(\cdot 2\),
J. Algebra 84 (1983), 107114.
 The complex Leech lattice and the maximal subgroups of the Suzuki group,
J. Algebra 84 (1983), 151188.
 The maximal subgroups of Conway's group \(Co_1\),
J. Algebra 85 (1983), 144165.
 The geometry and maximal subgroups of the simple groups of A. Rudvalis and J.
Tits,
Proc. London Math. Soc. (3) 48, (1984), 533563.
 On maximal subgroups of the Fischer group \(Fi_{22}\), Math.
Proc. Cambridge Philos. Soc. 95 (1984), 197222.
 The subgroup structure of the Lyons group, Math. Proc. Cambridge
Philos. Soc. 95 (1984), 403409.
 On lexicographic codes of minimal distance 4,
Atti Sem. Mat. Fis. Univ. Modena 33 (1984), 125135.
 The maximal subgroups of the Lyons group, Math. Proc.
Cambridge Philos. Soc. 97 (1985), 433436.
 Maximal subgroups of automorphism groups of simple groups,
J. London Math. Soc. (2) 32 (1985), 460466.
 The maximal subgroups of the O'Nan group, J. Algebra 97 (1985),
467473.
 The geometry of the HallJanko group as a quaternionic reflection group,
Geom. Dedicata 20 (1986), 157173.
 Is \(J_1\) a subgroup of the Monster? Bull. London. Math. Soc.
18 (1986), 349350.
 (with S. P. Norton) The maximal subgroups of the HaradaNorton group,
J. Algebra 103 (1986), 362376.
 Some subgroups of the Baby Monster, Invent. Math. 89 (1987), 197218.
 The local subgroups of the Fischer groups, J. London Math. Soc. (2)
36 (1987), 7794.
 (with P. B. Kleidman) A characterization of some locally finite simple
groups of Lie type, Arch. Math. 48 (1987), 1014.
 (with P. B. Kleidman) The maximal subgroups of \(Fi_{22}\), Math. Proc.
Cambridge Philos. Soc. 102 (1987), 1723.
Corrigendum, ibid. 103 (1988), 383.
 The oddlocal subgroups of the Monster,
J. Austral. Math. Soc. (A) 44 (1988), 116.
 Some subgroups of the Thompson group,
J. Austral. Math. Soc. (A) 44 (1988) 1732.
 On the 3local subgroups of Conway's group \(Co_1\),
J. Algebra 113 (1988), 261262.
 (with J. H. Conway and P. B. Kleidman) New families of ovoids in \(O_8^+\),
Geom. Dedicata 26 (1988), 157170.
 (with P. B. Kleidman) The maximal subgroups of \(J_4\), Proc. London
Math. Soc. (3) 56 (1988), 484510.
 (with P. B. Kleidman and R. A. Parker) The maximal subgroups of the Fischer
group \(Fi_{23}\), J. London Math. Soc. (2) 39 (1989), 89101.
 Vector stabilizers and subgroups of Leech lattice groups,
J. Algebra 127 (1989), 387408.
 (with S. P. Norton) The maximal subgroups of \(F_4(2)\) and its automorphism
group, Comm. Algebra 17 (1989), 28092824.
 (with P. B. Kleidman) The maximal subgroups of \(E_6(2)\) and
\(\mathrm{Aut}(E_6(2))\),
Proc. London Math. Soc. (3) 60 (1990), 266294.
 The 2 and 3 modular characters of \(J_3\), its covering group and
automorphism group, J. Symbolic Comput. 10 (1990), 647656.
 (with R. A. Parker) The computer construction of matrix representations
of finite groups over finite fields, J. Symbolic Comput. 9 (1990), 583590.
 (with P. B. Kleidman) \(J_3 < E_6(4)\) and \(M_{12} < E_6(5)\),
J. London Math. Soc. (2) 42 (1990), 555561.
 (with S. A. Linton) The maximal subgroups of the Fischer groups
\(Fi_{24}\) and \(Fi_{24}'\), Proc. London Math. Soc. (3) 63 (1991), 113164.
 (with I. A. I. Suleiman) Computer construction of matrix
representations of the covering group of the HigmanSims group,
J. Algebra 148 (1992), 219224.
 (with I. A. I. Suleiman) The 3 and 5modular characters of the
covering and automorphism groups of the HigmanSims group,
J. Algebra 148 (1992), 225242.
 (with I. A. I. Suleiman) The 3modular 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. 422437.
 (with M. D. E. Conder and A. J. Woldar) The symmetric genus of sporadic
groups, Proc. Amer. Math. Soc. 116 (1992), 653663.
 Some new subgroups of the Baby Monster, Bull. London Math. Soc.
25 (1993), 2328.
 Matrix generators for Fischer's group \(Fi_{24}\),
Math. Proc. Cambridge Philos. Soc. 113 (1993), 58.
 The Brauer tree for \(J_3\) in characteristic 17,
J. Symbolic Comput. 15 (1993), 325330.
 (with P. B. Kleidman) Sporadic simple subgroups of finite exceptional
groups of Lie type, J. Algebra 157 (1993), 316330.
 A new construction of the Baby Monster, and its applications,
Bull. London Math. Soc. 25 (1993), 431437.
 The symmetric genus of the Baby Monster, Quart. J. Math. (Oxford) 44
(1993), 513516.
 More on the maximal subgroups of the Baby Monster,
Arch. Math. (Basel) 61 (1993), 497507.
 The action of a maximal parabolic subgroup on the transpositions of the Baby
Monster,
Proc. Edinburgh Math. Soc. 37 (1993), 185189.
 (with I. A. I. Suleiman) Construction of the fourfold cover of the Mathieu
group
\(M_{22}\), Experimental Math. 2 (1993), 1114.
 (with I. A. I. Suleiman) The 2modular characters of Conway's second
group \(Co_2\), Math. Proc. Cambridge Philos. Soc. 116 (1994), 275283.
 (with A. J. E. Ryba) Matrix generators for the HaradaNorton group,
Experimental Math. 3 (1994), 137145.
 (with I. A. I. Suleiman) Standard generators for \(J_3\),
Experimental Math. 4 (1995), 1118.
 (with C. Jansen) The minimal faithful
3modular representation for the Lyons group,
Comm. Algebra 24 (1996), 873879.
 Standard generators for sporadic simple groups,
J. Algebra 184 (1996), 505515.
 The symmetric genus of the Fischer group \(Fi_{23}\), Topology
36 (1996), 379380.
 (with I. A. I. Suleiman) The 2modular characters of Conway's
third group \(Co_3\), J. Symbolic Comput. 24 (1997), 493506.
 (with C. Jansen) Two new constructions of the O'Nan group,
J. London Math. Soc. 56 (1997), 579583.
 (with I. A. I. Suleiman), Covering and automorphism groups of \(U_6(2)\),
Quart. J. Math. (Oxford) 48 (1997), 511517.
 (with C. Jansen) The 2modular and 3modular decomposition
numbers for the sporadic simple O'Nan group and its triple cover,
J. London Math. Soc. 57 (1998), 7190.
 An atlas of sporadic group representations,
in The Atlas 10 years on (eds. R. T. Curtis and R. A. Wilson), pp. 261273.
LMS Lecture Note Series 249, Cambridge University Press, 1998.
 A representation for the Lyons group in \(GL_{2480}(4)\), and a new
uniqueness proof, Arch. Math. (Basel) 70 (1998), 1115.
 (with S. A. Linton, R. A. Parker and P. G. Walsh)
Computer construction of the Monster,
J. Group Theory 1 (1998), 307337.
 The McKay conjecture is true for the sporadic simple groups,
J. Algebra 207 (1998), 294305.
 (with I. A. I. Suleiman), Construction of exceptional covers of generic
groups,
Math. Proc. Cambridge Philos. Soc. 125 (1999), 3138.
 The maximal subgroups of the Baby Monster, I, J. Algebra
211 (1999), 114.
 (with J. Saxl and D. B. Wales),
Embeddings of \(Sz(32)\) in \(E_8({\mathbb F})\),
Bull. London Math. Soc. 32 (2000), 196202.
 (with R. A. Parker), Constructions of Fischer's Baby Monster over
fields of characteristic not 2.
J. Algebra 229 (2000), 109117.
 (with I. A. I. Suleiman and P. G. Walsh),
Conjugacy classes in sporadic simple groups,
Comm. Algebra 28 (2000), 32093222.
 (with G. Havas and L. H. Soicher), A presentation for the Thompson
sporadic simple group, pp. 193200 in Groups and Computation III
(eds. W. M. Kantor and A. Seress), Proceedings of the International Conference
at the Ohio State University, June 1519, 1999. W. de Gruyter, 2001.
 (with J. N. Bray, I. A. I. Suleiman and P. G. Walsh),
Generating maximal subgroups of sporadic simple groups,
Comm. Algebra 29 (2001), 13251337.
 The Monster is a Hurwitz group,
J. Group Theory 4 (2001), 367374.
 (with S. P. Norton), Anatomy of the Monster, II,
Proc. London Math. Soc. 84 (2002), 581598.
 (with P. E. Holmes), A new maximal subgroup of the Monster,
J. Algebra 251 (2002), 435447.
 (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), 1833.
 Conjugacy class representatives in
Fischer's Baby Monster, LMS JCM 5 (2002), 175180.
 (with P. E. Holmes), A new computer construction of the Monster using
2local subgroups, J. London Math. Soc. 67 (2003), 349364.
 (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), 119140.
 (with P. E. Holmes) \(PSL_2(59)\) is a subgroup of the
Monster, J. London Math. Soc. 69 (2004), 141152.
 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), 120166. Copyright held by the authors.
Published by Cambridge Journals Online
under nonexclusive licence.
 Semipresentations for sporadic simple groups;
S.J.Nickerson, R.A.Wilson; Experimental Math. 14 (2005), 359371.
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), 205216. Copyright held by the authors.
Supplementary material: Readme file,
tar file.
Published by Cambridge Journals Online
under nonexclusive licence.
 On the orders of automorphism groups of finite groups;
J.N.Bray, R.A.Wilson; Bull. London Math. Soc. 37 (2005), 381385.
 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), 179186.
 Explicit construction of maximal subgroups of the Monster;
J.N.Bray, R.A.Wilson; J. Algebra 300 (2006), 835857.
 On the orders of automorphism groups of finite groups. II;
J.N.Bray, R.A.Wilson; J. Group Theory 9 (2006), 537545.
 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), 7596.

The character table of a maximal subgroup of the Monster; R. W. Barraclough, R. A. Wilson;
LMS J. Comput. Math. 10 (2007), 161175 (electronic).
Supplementary material: Readme file,
tar file.
Copyright held by the authors.
Published by Cambridge Journals Online
under nonexclusive licence.
 On subgroups of the Monster containing \(A_5\)s;
P.E. Holmes and R. A. Wilson;
J. Algebra 319 (2008), 26532667.

Constructive membership in blackbox groups;
P.E. Holmes, S.A. Linton, E.A. O'Brien, A.J.E. Ryba, and R.A. Wilson;
J. Group Theory 11 (2008), 747763.

Examples of 3dimensional 1cohomology for absolutely irreducible
modules of finite simple groups;
J.N.Bray, R.A.Wilson; J. Group Theory 11 (2008), 669673.

Octonions and the Leech lattice;
R.A.Wilson; J. Algebra 322 (2009), 21862190
.
The published version can be found here.
This page is maintained by Robert Wilson.
Last updated 23 November 2015.