A graph Γ is said to be locally (G, 2)-arc transitive for G a subgroup of Aut(Γ) if, for any vertex α of Γ, G is transitive on the 2-arcs of Γ starting at α. In this talk, we will discuss general results involving locally (G, 2)-arc transitive graphs and recent progress toward the classification of the locally (G, 2)-arc transitive graphs, where Sz(q) ≤ G ≤ Aut(Sz(q)), q = 2 for some k ∈ N. In ...

Let G be a collineation group of a thick finite generalised hexagon or generalised octagon Γ. If G acts primitively on the points of Γ, then a recent result of Bamberg et al. shows that G must be an almost simple group of Lie type. We show that, furthermore, the minimal normal subgroup S of G cannot be a Suzuki group or a Ree group of type G2, and that if S is a Ree group of type F4, then Γ is ...

This paper investigates the automorphism group of a connected and undirected G-symmetric graph Γ where G is an almost simple group with socle T . First we prove that, for an arbitrary subgroup M of AutΓ containing G, either T is normal in M or T is a subgroup of the alternating group Ak of degree k = |Mα : Tα| − |NM (T ) : T |. Then we describe the structure of the full automorphism group of G-...

In fact, this is a question about infinite simple groups because it is easy for G finite, and because a non-trivial normal subgroup gives rise to a non-trivial ideal different from the augmentation ideal. Also note that the problem reduces easily to the question on when the augmentation ideal is simple as a ring. The first interesting class of groups with almost simple FG was discovered in [3]....

Let G be a finite group. We denote by Γ(G) the prime graph of G. Let S be a sporadic simple group. M. Hagie in (Hagie, M. (2003), The prime graph of a sporadic simple group, Comm. Algebra, 31: 44054424) determined finite groups G satisfying Γ(G) = Γ(S). In this paper we determine finite groups G such that Γ(G) = Γ(A) where A is an almost sporadic simple group, except Aut(McL) and Aut(J2).