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    Liebeck MW, 1998,

    Regular orbits and the k(GV)-problem

    , Groups and Geometries, Pages: 145-148
    Liebeck MW, Seitz GM, 1998,

    On the subgroup structure of classical groups

    , Inventiones Mathematicae, Vol: 134, Pages: 427-453, ISSN: 0020-9910
    Evans DM, 1997,

    An infinite highly arc-transitive digraph

    , European Journal of Combinatorics, Vol: 18, Pages: 281-286, ISSN: 0195-6698
    Evans DM, 1997,

    Computation of first cohomology groups of finite covers

    , Journal of Algebra, Vol: 193, Pages: 214-238, ISSN: 0021-8693

    We give several applications of standard methods of group cohomology to some problems arising in model theory concerning finite covers. We prove a conjecture of the author that for G-finite, א0-categorical structures the kernels of minimal superlinked finite covers have bounded rank. We show that the cohomology groups associated to finite covers of certain structures (amongst them, the primitive, countable, totally categorical structures) have to be finite. From this we deduce that the finite covers of these structures are determined up to finitely many possibilities by their kernels. © 1997 Academic Press.

    Evans DM, 1997,

    Finite covers with finite kernels

    , Annals of Pure and Applied Logic, Vol: 88, Pages: 109-147, ISSN: 0168-0072

    We are concerned with the following problem. Suppose Γ and Σ are closed permutation groups on infinite sets C and W and ρ : Γ → Σ is a non-split, continuous epimorphism with finite kernel. Describe (for fixed Σ) the possibilities for ρ. Here, we consider the case where ρ arises from a finite cover π:C→W. We give reasonably general conditions on the permutation structure 〈W;Σ〉 which allow us to prove that these covers arise in two possible ways. The first way, reminiscent of covers of topological spaces, is as a covering of some Σ-invariant digraph on W. The second construction is less easy to describe, but produces the most familiar of these types of covers: a vector space covering its projective space.

    Guralnick RM, Liebeck MW, Macpherson D, Seitz GMet al., 1997,

    Modules for algebraic groups with finitely many orbits on subspaces

    , JOURNAL OF ALGEBRA, Vol: 196, Pages: 211-250, ISSN: 0021-8693
    Liebeck MW, Purvis CW, 1997,

    On the genus of a finite classical group

    , BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 29, Pages: 159-164, ISSN: 0024-6093
    Liebeck MW, Pyber L, 1997,

    Upper bounds for the number of conjugacy classes of a finite group

    , JOURNAL OF ALGEBRA, Vol: 198, Pages: 538-562, ISSN: 0021-8693
    Evans DM, 1996,

    Splitting of finite covers of א<inf>0</inf>-categorical structures

    , Journal of the London Mathematical Society, Vol: 54, Pages: 210-226, ISSN: 0024-6107

    Suppose that W is a countable א0-categorical structure. We investigate the question as to whether every finite cover of W splits, that is, has an expansion which is a trivial finite cover of W. We show that for most primitive structures W which are homogeneous for a single binary relation (homogeneous graphs, partial orderings, the Henson digraphs, ...) any finite cover splits. However, in contrast to this, we show that there are non-split covers (with finite kernels) of the countable, universal, homogeneous local order.

    Liebeck MW, 1996,

    Regular orbits of linear groups

    , JOURNAL OF ALGEBRA, Vol: 184, Pages: 1136-1142, ISSN: 0021-8693

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