Permutation groups are one of the oldest topics in algebra. Their study has recently been
revolutionized by new developments, particularly the Classification of Finite Simple Groups …

The first part of this paper surveys generating functions methods in the study of random
matrices over finite fields, explaining how they arose from theoretical need. Then we …

The base size of a permutation group, and the metric dimension of a graph, are two of a
number of related parameters of groups, graphs, coherent configurations and association …

We prove that in every finitely generated profinite group, every subgroup of finite index is
open; this implies that the topology on such groups is determined by the algebraic structure …

For every finite quasisimple group of Lie type G, every irreducible character χ of G, and every
element g of G, we give an exponential upper bound for the character ratio |χ(g)|/χ(1) with …

For each finite simple group G there is a conjugacy class CG such that each nontrivial
element of G generates G together with any of more than 1/10 of the members of CG …

Let G be a finite simple group and let S be a normal subset of G. We determine the diameter
of the Cayley graph Γ (G, S) associated with G and S, up to a multiplicative constant. Many …

The study of fixed point ratios is a classical topic in permutation group theory, with a long
history stretching back to the origins of the subject in the 19th century. Fixed point ratios …

The classical Waring problem deals with expressing every natural number as a sum of g (k)
k-th powers. Recently there has been considerable interest in similar questions for non …

Let G be a permutation group acting on a set Ω. A subset of Ω is a base for G if its pointwise
stabilizer in G is trivial. We write b (G) for the minimal size of a base for G. We determine the …