We determine upper bounds for the maximum order of an element of a finite almost simple
group with socle $ T $ in terms of the minimum index $ m (T) $ of a maximal subgroup of $ T …

For each finite classical group G, we classify the subgroups of G which act transitively on a G-
invariant set of subspaces of the natural module, where the subspaces are either totally …

Let S be a finite thick generalized quadrangle, and suppose that G is an automorphism
group of S. If G acts primitively on both the points and lines of S, then it is known that G must …

We classify the distance-regular Cayley graphs with least eigenvalue-2-2 and diameter at
most three. Besides sporadic examples, these comprise of the lattice graphs, certain …

We consider the problem of which distance-regular graphs with small valency are Cayley
graphs. We determine the distance-regular Cayley graphs with valency at most $4 $, the …

A pseudo‐hyperoval of a projective space, q even, is a set of subspaces of dimension such
that any three span the whole space. We prove that a pseudo‐hyperoval with an irreducible …

A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or
semiregular. Interest in this class of groups is motivated by two sources: problems arising in …

Let G be a group of collineations of a finite thick generalised quadrangle Γ. Suppose that G
acts primitively on the point set 𝒫 of Γ, and transitively on the lines of Γ. We show that the …

The classification of flag-transitive generalized quadrangles is a long-standing open
problem at the interface of finite geometry and permutation group theory. Given that all …

A generalised quadrangle is a point–line incidence geometry G such that:(i) any two points
lie on at most one line, and (ii) given a line L and a point p not incident with L, there is a …