Let 0 be a simple graph and let G be a group of automorphisms of 0. The graph is (G, 2)-arc transitive if G is transitive on the set of the 2-arcs of 0. In this paper we construct a new family of (PSU(3, q2), 2)-arc transitive graphs 0 of valency 9 such that Aut0 = Z3.G, for some almost simple group G with socle PSU(3, q2). This gives a new infinite family of non-quasiprimitive almost simple gr...

We describe a significantly improved algorithm for computing the conjugacy classes of a finite permutation group with trivial soluble radical. We rely on existing methods for groups that are almost simple, and we are concerned here only with the reduction of the general case to the almost simple case. Dedicated to Charles Leedham-Green on the occasion of his 65th birthday

Let $G$ be a finite group and $pi(G)$ be the set of all the prime‎ ‎divisors of $|G|$‎. ‎The prime graph of $G$ is a simple graph‎ ‎$Gamma(G)$ whose vertex set is $pi(G)$ and two distinct vertices‎ ‎$p$ and $q$ are joined by an edge if and only if $G$ has an‎ ‎element of order $pq$‎, ‎and in this case we will write $psim q$‎. ‎The degree of $p$ is the number of vertices adjacent to $p$ and is‎ ...

Let G be a permutation group on a finite set Ω. A base for G is a subset B ⊆ Ω with pointwise stabilizer in G that is trivial; we write b(G) for the smallest size of a base for G. In this paper we prove that b(G) ! 6 if G is an almost simple group of exceptional Lie type and Ω is a primitive faithful G-set. An important consequence of this result, when combined with other recent work, is that b...

Suppose that an automorphism group G acts flag-transitively on a finite generalized hexagon or octagon S, and suppose that the action on both the point and line set is primitive. We show that G is an almost simple group of Lie type, that is, the socle of G is a simple Chevalley group.

let $g$ be a finite group and $pi(g)$ be the set of all the prime‎ ‎divisors of $|g|$‎. ‎the prime graph of $g$ is a simple graph‎ ‎$gamma(g)$ whose vertex set is $pi(g)$ and two distinct vertices‎ ‎$p$ and $q$ are joined by an edge if and only if $g$ has an‎ ‎element of order $pq$‎, ‎and in this case we will write $psim q$‎. ‎the degree of $p$ is the number of vertices adjacent to $p$ and is‎ ...