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Analysing Finite Locally s-arc Transitive Graphs
We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms G and are either locally (G, s)-arc transitive for s > 2 or G-locally primitive. SuchExpand
Quasiprimitive groups with no fixed point free elements of prime order
The paper determines all permutation groups with a transitive minimal normal subgroup that have no fixed point free elements of prime order. All such groups are primitive and are wreath products in aExpand
Factorisations of sporadic simple groups
Abstract We determine all factorisations G = A B where the socle of G is a sporadic simple group.
Completely Transitive Codes in Hamming Graphs
A code in a graph ? is a non-empty subset C of the vertex set V of ?. Given C, the partition of V according to the distance of the vertices away from C is called the distance partition of C. AExpand
Small Maximal Sum-Free Sets
We determine all groups with a maximal (by inclusion) sum-free set of size at most 2 and all of size 3 where there exists a ∈ S. Expand
Transitive Permutation Groups Without Semiregular Subgroups
A transitive nite permutation group is called elusive if it contains no nontrivial semiregular subgroup. The purpose of the paper is to collect known information about elusive groups. The mainExpand
New Constructions of Groups Without Semiregular Subgroups
An elusive permutation group is a transitive permutation group with no fixed point free elements of prime order, or equivalently, no nontrivial semiregular subgroups. We provide several newExpand
Point regular groups of automorphisms of generalised quadrangles
We study the point regular groups of automorphisms of some of the known generalised quadrangles and show that they are much wilder than previously thought. Expand
Finite primitive permutation groups and regular cycles of their elements
We conjecture that if G is a finite primitive group and if g is an element of G, then either the element g has a cycle of length equal to its order, or for some r,m and k, the group GSym(m)wrSym(r),Expand
An infinite family of biquasiprimitive 2-arc transitive cubic graphs
A new infinite family of bipartite cubic 3-arc transitive graphs is constructed and studied. They provide the first known examples admitting a 2-arc transitive vertex-biquasiprimitive group ofExpand