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  • Journal article
    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.

  • Journal article
    Liebeck MW, Seitz GM, 1996,

    Reductive subgroups of exceptional algebraic groups

    , Memoirs of the American Mathematical Society, Vol: 121, Pages: 1-111, ISSN: 0065-9266
  • Journal article
    Liebeck MW, Shalev A, 1996,

    Classical groups, probabilistic methods, and the (2,3)-generation problem

    , Annals of Mathematics- Second Series, Vol: 144, Pages: 77-125, ISSN: 0003-486X
  • Journal article
    LIEBECK MW, SHALEV A, 1995,

    THE PROBABILITY OF GENERATING A FINITE SIMPLE-GROUP

    , GEOMETRIAE DEDICATA, Vol: 56, Pages: 103-113, ISSN: 0046-5755
  • Journal article
    Evans DM, Hrushovski E, 1995,

    The automorphism group of the combinatorial geometry of an algebraically closed field

    , Journal of the London Mathematical Society, Vol: 52, Pages: 209-225, ISSN: 0024-6107
  • Conference paper
    LIEBECK MW, SEITZ GM, 1995,

    Subgroups of exceptional algebraic groups

    , Conference on Groups of Lie Type and Their Geometries, Publisher: CAMBRIDGE UNIV PRESS, Pages: 151-156, ISSN: 0076-0552
  • Conference paper
    LIEBECK MW, 1995,

    Subgroups of simple algebraic groups and of related finite and locally finite groups of Lie type

    , NATO Advanced Study Institute on Finite and Locally Finite Groups, Publisher: KLUWER ACADEMIC PUBL, Pages: 71-96, ISSN: 0258-2023
  • Journal article
    LIEBECK MW, SEITZ GM, 1994,

    SUBGROUPS GENERATED BY ROOT ELEMENTS IN GROUPS OF LIE TYPE

    , ANNALS OF MATHEMATICS, Vol: 139, Pages: 293-361, ISSN: 0003-486X
  • Journal article
    Evans DM, Hrushovski E, 1993,

    On the automorphism groups of finite covers

    , Annals of Pure and Applied Logic, Vol: 62, Pages: 83-112, ISSN: 0168-0072

    We are concerned with identifying by how much a finite cover of an א0-categorical structure differs from a sequence of free covers. The main results show that (in the best circumstances) this is measured by automorphism groups which are nilpotent-by-abelian. In the language of covers, these results say that every finite (regular) cover can be decomposed naturally into linked, superlinked and free covers. The superlinked covers arise from covers over a different base, and to describe this properly we introduce the notion of a quasi-cover. These results generalise results of the second author obtained in the case where the base of the cover is a grassmannian of a disintegrated set. They also give a complete proof of a statement of the second author extending this case to the case of a grassmannian of a modular set. To do this, we need to analyse the possible superlinked covers of such a set. We also give a combinatorial condition on the base of a cover which guarantees various chain conditions on finite covers over this base, and introduce a pregeometry which is useful in the analysis of finite covers with simple fibre groups. © 1993.

  • Journal article
    Evans DM, Siemons J, 1993,

    On the number of orbits of a group in two permutation actions

    , Archiv der Mathematik, Vol: 60, Pages: 420-424, ISSN: 0003-889X

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