Given a finite group G and a set A of generators, the diameter diam (Γ (G, A)) of the Cayley
graph Γ (G, A) is the smallest ℓ such that every element of G can be expressed as a word of …

Permutation groups, their fundamental theory and applications are discussed in this
introductory book. It focuses on those groups that are most useful for studying symmetric …

This is a survey of methods developed in the last few years to prove results on growth in non-
commutative groups. These techniques have their roots in both additive combinatorics and …

Let (X n) be an unbounded sequence of finite, connected, vertex transitive graphs such that|
X n|= O (diam (X n) q) for some q> 0. We show that up to taking a subsequence, and after …

Let be a connected-vertex-transitive graph, let be a vertex of and let be the permutation
group induced by the action of the vertex-stabilizer on the neighbourhood. The graph is said …

By now, we have a product theorem in every finite simple group G of Lie type, with the
strength of the bound depending only in the rank of G. Such theorems have numerous …

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 …

We develop a new framework for analysing finite connected, oriented graphs of valency 4,
which admit a vertex-transitive and edge-transitive group of automorphisms preserving the …

In this paper we are concerned with the conjecture that, for any set of generators S of the
symmetric group Sym(n), the word length in terms of S of every permutation is bounded …

Let Γ be a connected G-vertex-transitive graph and let v be a vertex of Γ. The graph Γ is said
to be G-locally primitive if the action of the vertex-stabiliser Gv on the neighbourhood Γ (v) of …