Eamonn O'Brien - Papers

Older papers are available here in pdf format. More recent papers are on arXiV.

Comments, criticisms, requests for other papers not currently available here or for papers in different formats can be sent to:
e.obrien@auckland.ac.nz
Last updated: July 2023
The p-group generation algorithm
J. Symbolic Comput. 9, 677-698.
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The groups of order 256
J. Algebra 143, 219-235, 1991.
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Isomorphism testing for p-groups
J. Symbolic Comput. 17, 133-147, 1994.
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The fixity of groups of prime-power order
with M.F. Newman, Aner Shalev
Bull. London Math. Soc. 27 (2), 225-231, 1995.
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Generating random elements of a finite group
with Frank Celler, C.R. Leedham-Green, Scott H. Murray, Alice C. Niemeyer
Comm. Algebra 23, 4931-4948, 1995.
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Testing primitivity for matrix groups
with Derek F. Holt, C.R. Leedham-Green, Sarah Rees
J. Algebra 184 (3), 795-817, 1996.
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Computing decompositions for modules with respect to a normal subgroup
with Derek F. Holt, C.R. Leedham-Green, Sarah Rees
J. Algebra 184 (3), 818-838, 1996.
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Groups of deficiency zero
with George Havas, M.F. Newman
Geometric and Computational Perspectives on Infinite Groups, Amer. Math. Soc. DIMACS Series25, (DIMACS, 1994), pp. 53-67.
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Application of computers to questions like those of Burnside, II
with M.F. Newman
Internat. J. Algebra Comput. 6, 593-605, 1996.
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Tensor Products are Projective Geometries
with C.R. Leedham-Green
J. Algebra 189, 514-528, 1997.
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Recognising tensor products of matrix groups
with C.R. Leedham-Green
Internat. J. Algebra Comput. 7, 541-559, 1997.
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Classifying 2-groups using coclass
with M.F. Newman
Trans. Amer. Math. Soc. 351, 131-169, 1999.
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A local strategy to decide the Alperin and Dade conjectures
with Jianbei An
J. Algebra 206, 183-207, 1998.
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Certain cyclically presented groups are isomorphic
with A.C. Kim, D.L. Johnson
Comm. Algebra 27, 3531-3536, 1999.
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2-generator arithmetic Kleinian groups III
with M.D.E. Conder, C. Maclachlan, G.J. Martin
Math. Scand. 90, 161-179, 2002.
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The Alperin and Dade conjectures for the Fischer simple group Fi23
with Jianbei An
Internat. J. Algebra Comput. 6, 621-670, 1999.
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Enumerating p-groups
with Bettina Eick
J. Austral. Math. Soc. Ser. A67, 191-205, 1999.
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Computing 2-cocycles for central extensions and relative difference sets
with Dane Flannery
Comm. Alg. 28, 1935-1955, 2000.
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The Alperin and Dade conjectures for the O'Nan and Rudvalis simple groups
with Jianbei An
Comm. Alg. 30, 1305-1348, 2002.
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The groups of order at most 2000
with Hans Ulrich Besche, Bettina Eick
Electron. Research Announc. Amer. Math. Soc. 7, 1-4, 2001.
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A millennium project: constructing small groups
with Hans Ulrich Besche, Bettina Eick
Internat. J. Algebra Comput. 12 (5), 623-644, 2002.
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Constructing automorphism groups of p-groups
with Bettina Eick, C.R. Leedham-Green
Comm. Algebra 30, 2271-2295, 2002.
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Recognising tensor-induced matrix groups
with C.R. Leedham-Green
J. of Algebra 253, 14-30, 2002.
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The 2-generator restricted Burnside group of exponent 7
with M.R. Vaughan-Lee
Internat. J. Algebra Comput. 12, 575-592, 2002.
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The Alperin weight conjecture and Dade's conjecture for the simple group J4
with Jianbei An, R.A. Wilson
LMS JCM 6, 119-1140. [This paper is available from http://www.lms.ac.uk/jcm/6/lms2003-003]
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Conjectures on character degrees for the Harada-Norton simple group HN
with Jianbei An
Israel J. Math. 137, 157-181, 2003.
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On the efficiency of some finite groups
with M.F. Newman, George Havas
Comm. Algebra 32, 649-656, 2004.
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Groups and nilpotent Lie Rings whose order is the sixth power of a prime
with M.F. Newman, M.R. Vaughan-Lee
J. Algebra 278, 383-401, 2004.
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The groups of order p7 for odd prime p
with M.R. Vaughan-Lee
J. Algebra 292, 243-258, 2005
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Linear groups of small degree over finite fields
with Dane Flannery
Internat. J. Algebra Comput. 15, 467-502, 2005.
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The Alperin and Dade conjectures for the Fischer simple group Fi22
with Jianbei An
Comm. Algebra 33, 1529-1557, 2005.
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The Alperin and Dade conjectures for the Conway simple group Co1
with Jianbei An
Algebras and Representation Theory 7, 139-158, 2004.
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Constructive recognition of PSL(2, q)
with M.D.E. Conder, C.R. Leedham-Green
Trans. Amer. Math. Soc. 358, 1203-1221, 2006.
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Writing projective representations over subfields
with S.P. Glasby, C.R. Leedham-Green
J. Algebra 295, 51-61, 2006.
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Towards effective algorithms for linear groups
Finite Geometries, Groups and Computation, (Colorado), September 2004, 163--190, 2006.
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Certain Roman and flock generalized quadrangles have nonisomorphic elation groups
with George Havas, C.R. Leedham-Green, Michael C. Slattery
Advances in Geometry 6, 385--396, 2006.
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Not every p-group can be generated by elements of the same order
with Carlo M. Scoppola, M.R. Vaughan-Lee
Proc. Amer. Math. Soc. 134, 3457--3464, 2006.
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Constructive recognition of SL3(q)
with Frank Luebeck, Kay Magaard
J. Algebra 316, 619--633, 2007.
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A computer-assisted analysis of some matrix groups
with Derek F. Holt
J. Algebra 300, 199--212, 2006.
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The automorphism group of a binary self-dual doubly-even [72,36,16] code is solvable
with Stefka Bouyuklieva, Wolfgang Willems
IEEE Trans. Inform. Theory 52, 4244--4247, 2006.
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The class breadth conjecture revisited
with Bettina Eick, M.F. Newman
Journal of Algebra 300, 384--393, 2006.
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Finding the characteristic of a group of Lie type
with Martin W. Liebeck
J. Lond. Math. Soc. 75, 741--754, 2007.
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On intersections of classical groups
with Peter A. Brooksbank
J. Group Theory 11, 465--478, 2008.
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Constructing the group preserving a system of forms
with Peter A. Brooksbank
Internat. J. Algebra Comput. 18, 227--241, 2008.
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Counting groups: gnus, moas and other exotica
with John H. Conway, Heiko Dietrich
Math. Intelligencer 30, 6--15, 2008.
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Constructive membership in black-box groups
with P.E. Holmes, S.A. Linton, A.J.E. Ryba, R.A. Wilson
J. Group Theory 11, 747--763, 2008.
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On p-groups having the minimal number of conjugacy classes of maximal size
with A. Jaikin-Zapirain, M.F. Newman
Israel J. Math. 172, 119--123, 2009.
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Base sizes for sporadic simple groups
with Timothy C. Burness, Robert A. Wilson
Israel J. Math.177, 307--334, 2010.
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The Alperin weight conjecture and Dade's conjecture for the simple group Fi'24
with Jianbei An, John J. Cannon, W.R. Unger
LMS JCM 11, 100-145. [This paper is available from http://www.lms.ac.uk/jcm/11/lms2007-003]
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Constructive recognition of classical groups in odd characteristic
with C.R. Leedham-Green
Journal of Algebra 322, 833-881, 2009
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Recognition of small dimensional representations of general linear groups
with Kay Magaard, Akos Seress
J. Aust. Math. Soc. 85 , 229--250, 2008.
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On some questions about a family of cyclically presented groups
with Alberto Cavicchioli, Fulvia Spaggiari
J. Algebra 320, 4063--4072, 2008.
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Short presentations for alternating and symmetric groups
with J.N. Bray, M.D.E. Conder, C.R. Leedham-Green
Trans. Amer. Math. Soc. 363, 3277--3285, 2011.
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Deciding finiteness of matrix groups in positive characteristic
with A.S. Detinko, D.L. Flannery
J. Algebra 322, 4151--4160, 2009.
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The Ore Conjecture
with Martin W. Liebeck, Aner Shalev, Pham Huu Tiep
J. European Math. Soc. 12, 939--1008, 2010.
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Algorithms for matrix groups
Groups St Andrews 2009 in Bath, LMS Lecture Notes 388, 297--323, 2011.
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Finite 3-groups of class 3 whose elements commute with their automorphic images
with A. Abdollahi, A. Faghihi, S.A. Linton
Archiv der Mathematik 95, 1--7, 2010.
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Products of squares in finite simple groups
with Martin W. Liebeck, Aner Shalev, Pham Huu Tiep
Proc. Amer. Math. Soc. 140, 21--33, 2012.
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On the automorphism group of a binary self-dual doubly-even [72,36,16] code
with Wolfgang Willems
IEEE Trans. Inform. Theory 57, 4445 - 4451, 2011.
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Commutators in finite quasisimple groups
with Martin W. Liebeck, Aner Shalev, Pham Huu Tiep
Bull. London Math. Soc. 43, 1079--1092, 2011.
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Orbit invariants and an application to the Baby Monster
with Max Neunhoeffer, Felix Noeske, R.A. Wilson
J. Algebra 341, 297--305, 2011
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On the classification of groups of prime-power order by coclass: The 3-groups of coclass 2
with Bettina Eick, C.R. Leedham-Green, M.F. Newman
Internat. J. Algebra Comput. 23, 1243--1288, 2013
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Algorithms for the Tits Alternative and related problems
with A.S. Detinko, D.L. Flannery
J. Algebra 344, 397--406, 2011.
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Recognizing finite matrix groups over infinite fields
with A.S. Detinko, D.L. Flannery
J. Symbolic Comput. 50, 100--109, 2013.
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Some word maps that are non-surjective on infinitely many finite simple groups
with Sebastian Jambor, Martin W. Liebeck
Bull. Lond. Math. Soc. 45, 907--910, 2013.
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Constructive recognition of classical groups in even characteristic
with Heiko Dietrich, C.R. Leedham-Green, Frank Luebeck
Journal of Algebra 391, 227-255, 2013
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Algorithms for linear groups of finite rank
with A.S. Detinko, D.L. Flannery
J. Algebra 393, 187-196, 2013.
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Enumerating classes and characters of p-groups
with Christopher Voll
Trans. Amer. Math. Soc. 367, 7775--7796, 2015.
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A practical model for computation with matrix groups
with Henrik Baarnhielm, Derek F. Holt, C.R. Leedham-Green
J. Symbolic Comput. 68, 460--492, 2015.
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On the uniqueness of the generalized octagon of order (2,4)
with Arjeh M. Cohen, Sergey Shpectorov
Journal of Algebra 421, 363--393, 2015.
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Effective black-box constructive recognition of classical groups
with Heiko Dietrich, C.R. Leedham-Green
Journal of Algebra 421, 460--492, 2015.
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Recognition of finite exceptional groups of Lie type
with Martin W. Liebeck
Trans. Amer. Math. Soc. 368, 6189--6226, 2016.
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Regular orbits of symmetric and alternating groups
with Joanna B. Fawcett, Jan Saxl
J. Algebra 458, 21--52, 2016.
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Code loops in dimension at most 8
with Petr Vojtěchovský
J. Algebra 473, 607--626, 2017.
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Reliability and reproducibility of Atlas information
with Thomas Breuer, Gunter Malle
Finite Simple Groups: Thirty Years of the Atlas and Beyond, Contemporary Mathematics 694, 21--32, 2017.
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Unipotent class representatives for finite classical groups
with Samuel Gonshaw, Martin W. Liebeck
J. Group Theory 20, 505--525, 2017.
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Surjective word maps and Burnside's pa qb theorem
with Robert M. Guralnick, Martin W. Liebeck, Aner Shalev, Pham Huu Tiep
Invent. Math. , 2018.
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Constructing composition factors for a linear group in polynomial time
with Derek F. Holt, C.R. Leedham-Green
J. Algebra 361 , 2020.
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Last updated: July 2023

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