Publications
46 results found
Bryant RM, Evans DM, 1997, The small index property for free groups and relatively free groups, Journal of the London Mathematical Society, Vol: 55, Pages: 363-369, ISSN: 0024-6107
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- Citations: 22
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.
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
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- Citations: 7
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.
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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- Citations: 2
Camina AR, Evans DM, 1991, Some infinite permutation modules, Quarterly Journal of Mathematics, Vol: 42, Pages: 15-26, ISSN: 0033-5606
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- Citations: 11
Evans DM, 1991, The small index property for infinite dimensional classical groups, Journal of Algebra, Vol: 136, Pages: 248-264, ISSN: 0021-8693
We show that the countable dimensional analogues of the finite classical groups have the strong small index property. That is, if G is one of these groups and V is its natural module, and if H is a subgroup of G of index less than 2ω then there exists a finite dimensional subspace X of V such that H is sandwiched between the pointwise and setwise stabilisers in G of X. © 1991.
Evans DM, Hodges W, Hodkinson IM, 1991, Automorphisms of Bounded Abelian Groups, Forum Mathematicum, Vol: 3, Pages: 523-542, ISSN: 0933-7741
We show that if A is a countable abelian group of finite exponent, and H is a subgroup of index less than 2ωin the automorphism group Aut(A) of A, then H contains the pointwise stabiliser of some finite set of elements of A. (Thus A has the “small index property.”) We consider groups B which are direct sums of isomorphic cyclic p-groups Z (pm), together with subgroups A which are the corresponding sums of p-groups Z (/p) for some t < m. For these pairs of groups we determine exactly when it is true that each automorphism of A extends to an automorphism of B, so that the extensions form an embedding of Aut(A) in Aut(B). Finally we discuss several connections between these results and questions in set theory and model theory. © de Gruyter 1991
Evans DM, Hrushovski E, 1991, Projective planes in algebraically closed fields, Proceedings of the London Mathematical Society, Vol: s3-62, Pages: 1-24, ISSN: 0024-6115
We investigate the combinatorial geometry obtained from algebraic closure over a fixed subfield in an algebraically closed field. The main result classifies the subgeometries which are isomorphic to projective planes. This is applied to give new examples of algebraic characteristic sets of matroids. The main technique used, which is motivated by classical projective geometry, is that a particular configuration of four lines and six points in the geometry indicates the presence of a connected one-dimensional algebraic group. © 1991 Oxford University Press.
Evans D, Pillay A, Poizat B, 1990, A group in a group, Algebra and Logic, Vol: 29, Pages: 244-252, ISSN: 0002-5232
1. In an Abelian group, a module, or more generally a one-based group H, the only definable groups are the obvious ones: if G is interpretable in H, then it has a definable subgroup of finite index which is definably isomorphic to a quotient A/B, where A and B are definable subgroups of a Cartesian power of H. 2. In such a group the introduction of those quotient groups weakly eliminates imaginary elements. More generally, for a stable theory the existence of canonical real bases for complete types implies the elimination of imaginary elements. 3. A group which is interpretable in a one-based structure is one-based. The property of being one-based is preserved by interpretation for theories of finite rank but not in general. © 1991 Plenum Publishing Corporation.
Evans DM, Hewitt PR, 1990, Counterexamples to a conjecture on relative categoricity, Annals of Pure and Applied Logic, Vol: 46, Pages: 201-209, ISSN: 0168-0072
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- Citations: 19
Evans DM, 1987, A note on automorphism groups of countably infinite structures, Archiv der Mathematik, Vol: 49, Pages: 479-483, ISSN: 0003-889X
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- Citations: 17
Evans DM, 1987, Infinite permutation groups and minimal sets, Quarterly Journal of Mathematics, Vol: 38, Pages: 461-471, ISSN: 0033-5606
Evans DM, 1986, Subgroups of small index in infinite general linear groups, Bulletin of the London Mathematical Society, Vol: 18, Pages: 587-590, ISSN: 0024-6093
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- Citations: 22
Evans DM, 1986, Homogeneous geometries, Proceedings of the London Mathematical Society, Vol: s3-52, Pages: 305-327, ISSN: 0024-6115
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- Citations: 12
Evans DM, 1985, The 7-modular representations of Janko's smallest simple group, Journal of Algebra, Vol: 96, Pages: 35-44, ISSN: 0021-8693
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- Citations: 1
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