Martin W. Liebeck

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Finite primitive permutation groups of rank 3 have been the subject of much study in the past twenty years, leading on the one hand to interesting new groups (for instance, some sporadic groups) and on the other to new techniques in the theory of permutation groups. It is readily seen that if G is a primitive rank 3 permutation group of finite degree n then(More)
A classification is given of primitive K 0-categorical structures which are smoothly approximated by a chain of finite homogeneous substructures. The proof uses the classification of finite simple groups and some representation theory. The main theorems give information about a class of structures more general than the X 0-categorical, co-stable structures(More)
Let G be a finite simple group and let S be a normal subset of G. We determine the diameter of the Cayley graph Γ(G, S) associated with G and S, up to a multiplicative constant. Many applications follow. For example, we deduce that there is a constant c such that every element of G is a product of c involutions (and we generalize this to elements of(More)
We extend a result of E. Hrushovski and A. Pillay as follows. Let G be a finite subgroup of GL(n, F) where F is a field of characteristic p such that p is sufficiently large compared to n. Assume that G is generated by p-elements. Then G is a product of 25 of its Sylow p-subgroups. If G is a simple group of Lie type in characteristic p, the analogous result(More)