Suppose r = pb, where p is a prime. Let V be an n-dimensional GF(r)-space and G a subgroup of AGL(V) ¿ AGL(n, r) containing all translations and acting primitively on the set of vectors in V. Denote by G0 the stabilizer in G of the zero vector, so that G0 = G L(V) ¿ G L(n, r) and G is the semidirect product of V and G0. Suppose that the generalized Fitting subgroup F*(G0) of G0 is an exceptional (twisted or untwisted, quasisimple) Chevalley group and that G is a graph structure on V on which G acts primitively and distance transitively. The content of this paper is that then G and G are known. This result solves an open case in the outstanding problem of classifying all finite primitive distance-transitive groups.
|Journal||Proceedings of the London Mathematical Society. Third series|
|Publication status||Published - 2001|