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Journal articleEvans DM, Ferreira MS, 2011,
The geometry of Hrushovski constructions, I: The uncollapsed case
, Annals of Pure and Applied Logic, Vol: 162, Pages: 474-488, ISSN: 0168-0072An intermediate stage in Hrushovski's construction of flat strongly minimal structures in a relational language L produces ω-stable structures of rank ω. We analyze the pregeometries given by forking on the regular type of rank ω in these structures. We show that varying L can affect the (local) isomorphism type of the pregeometry, but not its finite subpregeometries. A sequel will compare these to the pregeometries of the strongly minimal structures. © 2011 Elsevier B.V.
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Journal articleEvans DM, Pastori E, 2011,
Second cohomology groups and finite covers of infinite symmetric groups
, Journal of Algebra, Vol: 330, Pages: 221-233, ISSN: 0021-8693For Ω an infinite set, k≥2 and W the set of k-sets from Ω, there is a natural closed permutation group Γk which is a non-split extension 0→Z2W→Γk→Sym(Ω)→1. We classify the closed subgroups of Γk which project onto Sym(Ω). The question arises in model theory as a problem about finite covers, but here we formulate and solve it in algebraic terms. © 2011 Elsevier Inc.
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Journal articleLiebeck MW, Nikolov N, Shalev A, 2011,
Groups of Lie type as products of <i>SL</i><sub>2</sub> subgroups
, JOURNAL OF ALGEBRA, Vol: 326, Pages: 201-207, ISSN: 0021-8693- Author Web Link
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- Citations: 10
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Journal articleLiebeck MW, Litterick AJ, Marion C, 2011,
A rigid triple of conjugacy classes in <i>G</i><sub>2</sub>
, JOURNAL OF GROUP THEORY, Vol: 14, Pages: 31-35, ISSN: 1433-5883- Author Web Link
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- Citations: 7
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Journal articleLiebeck MW, Praeger CE, Saxl J, 2010,
Regular Subgroups of Primitive Permutation Groups
, MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 203, Pages: 1-+, ISSN: 0065-9266- Author Web Link
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- Citations: 22
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Journal articleLiebeck MW, Macpherson D, Tent K, 2010,
Primitive permutation groups of bounded orbital diameter
, PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, Vol: 100, Pages: 216-248, ISSN: 0024-6115- Author Web Link
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- Citations: 9
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Journal articleLiebeck MW, Nikolov N, Shalev A, 2010,
A conjecture on product decompositions in simple groups
, GROUPS GEOMETRY AND DYNAMICS, Vol: 4, Pages: 799-812, ISSN: 1661-7207- Author Web Link
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- Citations: 10
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Journal articleLiebeck MW, O'Brien EA, Shalev A, et al., 2010,
The Ore conjecture
, JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, Vol: 12, Pages: 939-1008, ISSN: 1435-9855- Author Web Link
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- Citations: 125
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Journal articleEvans DM, Wong MWHO, 2009,
Some remarks on generic structures
, Journal of Symbolic Logic, Vol: 74, Pages: 1143-1154, ISSN: 0022-4812We show that the N0-categorical structures produced by Hrushovski's predimension construction with a control function fit neatly into Shelah's SOPn hierarchy: if they are not simple, then they have SOP3 and NSOP4. We also show that structures produced without using a control function can be undecidable and have SOP. © 2009, Association for Symbolic Logic.
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Journal articleEmms J, Evans DM, 2009,
Constructing continuum many countable, primitive, unbalanced digraphs
, Discrete Mathematics, Vol: 309, Pages: 4475-4480, ISSN: 0012-365XWe construct continuum many non-isomorphic countable digraphs which are highly arc transitive, have finite out-valency and infinite in-valency, and whose automorphism groups are primitive. © 2009 Elsevier B.V. All rights reserved.
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